Your metal bowl sitting in your 70°F room is 70°F (at least, if its been sitting there for a bit). Your plastic bowl, or glass bowl, or ceramic bowl, or any other bowl sitting in the same room is also 70°F. They're all actually the same temperature.
Now, given, when you touch the metal bowl, it feels cooler than the plastic one. This is because your finger isn't 70°F, and your body heat is transferred away quicker by metal than (say) plastic.
If the dough is room temperature, it won't matter—heat isn't flowing out of it. The dough itself doesn't generate much heat. If your dough started above room temperature, it will cool a little quicker in a metal bowl. But, if you wanted to keep it from cooling, putting it in a warm place is much more effective.
A stainless steel bowl is fine. I'd avoid aluminum (and copper, if anyone makes a mixer with such a thing) due to them being reactive, especially if you're making sourdough.
The best recommendation I have seen is plain plastic wrap. If you have an oil mister, mist the wrap before using it. If you don't, pour oil into a bowl, enough to form a puddle, and toss your ball of dough in the oil. Then transfer your dough to the rising container (if you use the same bowl you used for oiling, take the dough out, pour out the superfluous oil, return the dough into the bowl). In the best case, the bowl will be deep enough for the dough to rise without the middle touching the wrap, but if it rises more (even with the dough pressing against the wrap), dough with enough gluten development will peel off the oiled wrap with minimal losses, even if it is wet.
The wrap will keep your dough surface moist in both the fridge and outside. It doesn't allow breathing, but this shouldn't be a concern in most cases. If you overyeast the dough, the collection of fermentation byproducts in the bowl will probably make for worse taste than if they are allowed to dissipate, but the correct solution for this problem is to not produce them in the first place. With your "very long times", this is probably not a problem in your case.
You can also use this method for the secondary fermentation. But in the final proofing stage, you have to make sure that your dough never rises enough to touch the wrap, or else the loaf will deform while you are removing the wrap. Also, if you are proofing in banettons, don't oil them, use flour combinations to prevent sticking.
If you are out of plastic wrap, substituting alu wrap is a bad idea, because yeast is very sensitive to metallic ions. Today's non-reactive metal utensils are safe enough for use with yeast dough, but untreated aluminium can be problematic. Try baking paper instead (you may have to tape it to the outer bowl walls).
Best Answer
Jay's answer of a couche is great for relatively long loaves like baguettes or even ciabatta. For oval or round loaves, however, you'll need support on more than two sides. In that case, the solution is a basket known as a banneton or brotform (depending on which language you prefer to make your bread in). Again, they are not for baking -- you dust them with flour and then gently flip them to get the dough out right before baking. (Note that this is how bakers often make those lovely patterns of rings of flour on the top of their loaves.)
If you don't use either, you may still be able to achieve greater height by shaping more fully. Many people have been cautioned by various books to shape very gently and avoid degassing. I spent years producing flabby flat loaves this way, thinking that the key to loaf height was avoiding degassing and letting the bubbles grow. But it's often the opposite: by leaving the bubbles too big and shaping gently, you don't stretch the gluten enough to provide support and the yeast actually grow more slowly since they are immersed in their own waste product gases. (The only time to shape gently is if the yeast isn't strong enough to raise the dough again, which can sometimes happen with long sourdough fermentations or with very rich doughs like brioche, for example.)
While it's good advice to avoid unnecessary degassing (you don't actually want to "punch down" the dough to shape it), the main way to achieve a tall loaf is by having a very taut "skin," and that generally can only happen if you shape forcefully to stretch that "skin" multiple times. When I make free-form loaves without a banneton or other support, I generally:
For more shaping advice, I'd recommend looking at Jeffrey Hamelman's Bread: A Baker's Book of Techniques and Recipes, which devotes a 30-page chapter to shaping techniques, with a lot of drawings to illustrate the individual steps for each particular loaf shape. (He also has another entire chapter on braiding techniques.)
Also, to increase the "strength" (elasticity) of the gluten in the dough, you could also try incorporating "stretch-and-fold" manipulations periodically during your bulk rise. This will prepare the gluten even more before shaping.
Lastly, using a baking stone or steel can help in inflating the dough fast enough in the oven before it has a chance to spread even more: you want the bubbles in the dough to blow up like a balloon quickly during baking. If they bake too slowly, the bubbles can collapse or the gluten will stretch out and allow the dough to slacken before the crust hardens.