Yes, oxygen (and sunlight) can affect the quality of oil. The oil turns rancid after some time. And storing the oil in a really airtight container (like a can from which air has been evacuated before sealing) should prevent or at least slow the process.
However, the problem is that you can't practically store your oil in an airless container and still use it. Yes, you can seal a bottle of oil. But there will still be air between the oil surface and the stopper, and the oxygen from this air will react with the oil molecules on the surface. And if you use a non-sealed bottle, the exactly same thing will happen. Unlike other cases (soda in a sealed vs. open bottle), the reaction of oil and oxygen isn't quick and aggressive enough to quickly exhaust the small amount of oxygen in a sealed bottle and stop. It will go on regardless of whether there is free air flow from the atmosphere or not.
So what can you do? You can still minimize the rate of rancidification. But it isn't the openness of the bottle that matters, it is the contact area size, because this is where the reaction takes place. Which means, store your oil in a (preferably tall and slim) bottle, as opposed to something like a jug. Protect it from light, because light is definitely damaging for oil. Also, buy it in small sizes, so you can go through it in a reasonably short time. And after all, don't worry too much about it. The reactions are slow, and the oils you use several times per week will not last long enough in your kitchen to deteriorate too much. It can become a problem if you collect special oils which are used seldom and contribute a significant part of the taste in a dish.
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:
- Elevated temp, plastic bag: no measurable weight loss
- Elevated temp, paper bag: ~7% weight loss
- Room temp, paper bag: ~4% weight loss
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.
Best Answer
Airtight packaging doesn't slow down bacteria growth. There are a few myths about them which don't apply in practice:
These two hold whether your food is in the fridge or not – so storing the food in an airtight container outside of the fridge doesn't change anything about its safety either. *
The one way it helps with food safety is an edge case: if you forget something until it molds or spoils, the now-high levels of pathogens won't contaminate something else, exposing it to more than the normal "background" level.
The airtight container doesn't help with food safety, but it is quite good for food quality and has other convenience aspects:
So the airtight containers are best practice for quality reasons. And non-air-tight containers, which have a loosely fitting lid (no visible holes, but also no gasket, such as a stock pot or a skillet covered with a lid) will give you about 80-90% of the desired effect.
* to be pedantic, it can interfere in one way: if you intend to store hot non-shelf-stable food outside for a short time, and are afraid it will enter the danger zone, a closed lid will slow down the time it cools down. But I suppose not many people keep a wireless temperature probe in their airtight container, so the point is quite moot in practice.