Pie is a good example: fruit pie tends to keep for a good while at room temperature. I have found many sites which stridently claim this not to be the case, and many grocery stores that leave their bakery pies at room temp for about three days (even psycho Mrs. Cookwell says 2 days is fine). I'm siding with the grocery stores. Nut pies tend to last longer still, because they're drier: the presence of dairy and eggs is counteracted by the higher concentration of sugar.
Likewise cake, though it can vary depending on your frosting...The more things besides fat and sugar in your frosting, the more it needs to be refrigerated. In most cases cake will stay edible longer than you'd want to eat it. Again, grocery stores only bother to refrigerate decorated cakes, or ones with cream cheese icing.
Most store bought condiments are fine at room temperature. Obviously not mayonnaise, or anything creamy, but ketchup, mustard, A-1, worstershire...They last a good long time unrefrigerated. Likewise soy sauce, fish sauce, and some of the more popular asian condiments.
I've never seen a pepper sauce (e.g. Tabasco) that needs refrigeration, and they'll last for years, though the color starts going off after a while.
There is no bacterial risk to leaving fruits and vegetables out, but this will dramatically increase the rate of spoilage. The exceptions are root vegetables, and bananas. Root vegetables will last a long time in a cool dark place, so just lump 'em in your garage if you're not going to eat them in the next week or two. And bananas will go south at the same rate regardless (though you can freeze them for future banana bread).
Fresh eggs (like, straight from the chicken) will last a couple of weeks without refrigeration (make sure they're not fertilized, or you may wake up to find baby chickens in your kitchen). The rule of thumb is "Every day unrefrigerated is like 5 days refrigerated." Once eggs are cracked, you should use them immediately.
I'd trust store bought eggs left out on the counter to eat, though its not good to let refrigerated eggs get warm again. Eggs have a wide array of natural antimicrobial tendencies, though the processing store bought eggs go through removes some of this. (citation). An easy way to test for internal contamination is to see if the egg floats in water. If it floats, toss it.
Bacon grease keeps a long time unrefrigerated, as does any sort of fat really, as long as it's strained and filtered. With fats you're more worried about them going rancid, which is a function of light and air (its a type of oxidation), so store your fat in a dark place, in a sealed container. (citation)
Butter can last several days unrefrigerated (it should be covered). I'd say as much as a week, but I have no way of knowing because it never lasts that long. It's much more likely to oxidize (see above) and go rancid than to pick up a significant bacterial colony.
What happens to bread when it is done
Yes, there is something particular what happens at a temperature in the mid-90s. Not all details of it are proven, but the major outline is, and the hypotheses about the details are solid enough to make it into textbooks.
Starch is contained in tiny granules, a few micrometers in diameter. When heated in the presence of water, there is a specific temperature at which these granules burst. The molecules of starch come in contact with water and the water molecules get lodged in the nooks and crannies of the much larger starch molecules. This process is called gelating.
You can observe it easily on the macro level. Just cook a bechamel or starch pudding on stovetop, stirring constantly. The liquid will stay rather thin until all will thicken at once, just before you see the first bubbles of boiling. This is when the starch gelates.
The same thing happens in bread too. This is why you want to heat the bread to this temperature. If you don't, you will have raw starch inside, which doesn't taste well.
The exact temperature at which this happens varies a bit with the type of starch. It is not the same for rice and wheat, for example, and I think that it is also a bit different between different wheat cultivars. But the range within this variation occurs is not so wide, all references I have seen move somewhere between 94 and 98 degrees Celsius. So the recipe author just picks a temperature he knows to work for the flour used in the bread, maybe also accounting for some additional heat transfer after taking out of the oven.
Can you use temperature as an indicator for doneness
The theory says yes. My personal experience also says yes. Why did you feel that your bread was too doughy? There are different reasons why this could have happened. You could have measured it wrong (with the probe being too close to the surface, where the temperature is higher). You could have cut it too early. (Bread is always doughy before the first starch retrogradation, which occurs maybe 1 hour after baking). It is also possible that the bread was actually done in the sense of gelled starch, but that the recipe produced a rather moist bread and that you have grown accustomed to dry breads if you normally bake your breads for a very long time, so your brain perceived the unaccustomed texture as "not right". Or it is possible that something went wrong with the leavening, making the bread too dense. Dense bread is always doughy, you cannot bake the moisture out of it.
technical criteria for bread doneness
There are two big chemical changes which happen to bread while baking. The proteins in bread (the gluten) have to harden. Before that, they are soft and pliable. At some temperature, they become rubber-like. The hardened gluten gives the bread structure.
The second change is the starch gelation I explained earlier. When this happens, the liquid part of the dough (dough consists of a liquid phase suspenede in the elastic gluten mesh) thickens. Gelated starch gives bread a fluffy, soft body.
As the starch gelates at much hicher temperatures than proteins denature, bread is taken out of the oven when the starch is done.
The third step is the starch retrogradation. In retrogradation, starch loses the water which it took during gelation. There are three big stages of it, after each the texture changes drastically. The first happens at about an hour after getting out of the oven. This is when the bread is considered done by textbooks. In practice, there are many people (including myself) who like the taste of the moist hot bread just out of the oven, and they consider it done at the previous step. The second happens after about 24 hours; after it, the bread is considered stale. The third step takes several days, and after it, bread is considered inedible, because it becomes hard as wood.
So technically, bread is considered done after it has been baked to gelation temperature and then left alone for 1 hour.
Best Answer
Summary:
If the loaf is kept at an elevated temperature in a plastic bag for a period of 6-12 hours I believe you will see little to no difference compared to storing at room temperature.
Stored at an elevated temperature in a paper bag the loaf will start to dry out to a noticeable extent.
Note that the answer below does not address possible food safety issues.
Long-winded details:
My previous answer provided some information up to 36°C (97°F). Since the question asks about the temperature range 35-55°C I did some amateurish experimentation of my own.
Using my fan assisted oven at the lowest setting, I halved a store bought sourdough loaf and placed one half in the oven overnight and kept the other half at room temperature (25°C).
I should note that my oven temperature fluctuates between ~37°C and ~47°C (99-117°F) measured using using a Thermapen at various intervals. I'll also note that I wrapped the loaf-half that went into the oven in a tea towel to protect it from the oven fan.
In the morning I taste tested the two loaf-halves. The room temperature loaf had started to stale slightly but the half from the oven had also started to dry out. It was noticeably more difficult to cut through the loaf-half from the oven and I saw about 8mm of visibly dried bread extending inwards from the outer surfaces.
This test was quite obviously flawed in that you would neither use a tea towel to wrap your bread whilst in the car, nor would you first cut the loaf in half.
The next experiment I did used 5 smaller loaves of the same variety, from the same store. I placed two in a plastic bag and two more in the paper bag in which the loaves were purchased. The fifth loaf I kept at room temperature in order to compare later.
Using the same oven setting I kept the bagged loaves in the oven for 6 hours. After six hours I removed two loaves, one from each bag, and taste tested.
Comparing a small slice of the loaf from the plastic bag to a slice from the room temperature loaf I sensed no obvious difference. The loaf from the paper bag was noticeably drier. I marked the loaves from the oven and saved them for comparison again later.
Keeping the remaining two loaves in the oven for a further 6 hours, I did another taste test this morning.
The loaf that had been kept at room temperature had now slightly but noticeably started to stale. Comparing this to the 12 hour loaf from the plastic bag I noticed hardly any difference. I really couldn't say whether one was less stale than the other. Comparing the 12 hour loaf from the paper bag, once again drying was pronounced.
I also made a second comparison using the loaves that had been taken out at 6 hours. Again I sensed no obvious difference between the loaf from the plastic bag and the room temperature loaf. The 6 hour loaf from the paper bag was no less dry than it had been 6 hours before.
Update:
I followed up on @Athanasius question from the comments and did another test with the oven fan switched off. This time I had to fight with the oven thermostat to stay within the temperature range but managed to stay just under 130°F. I tested three small loaves of the same variety and from the same store as the previous tests. Again, I kept two in the oven in paper and plastic bags, and one at room temperature (also in a paper bag). As well as taste testing I also weighed the loaves before and after the test. Here are the figures for weight loss after 6 hours:
While I don't have any objective means for comparing dryness from the previous experiment (I didn't weight the loaves in the previous test) it does seem like the oven fan led to increased drying. As a subjective measure I offer the fact that following yesterdays testing I discarded both the 6 hour and 12 hour loaves from the paper bag, but this morning I found the loaf from the paper bag good enough for breakfast despite the drying.
The words in the summary are, however, still correct: stored at an elevated temperature in a paper bag a loaf will start to dry out to a noticeable extent.