Question: During wintertime it is often cold enough in my apartment that proofing takes much longer than in summer. I'd like to use my oven to create a warmer environment, in which the dough would rise faster. I can go 30-50 degrees celsius, the question is what temperature is safe and at what temperature will I actually start baking the dough. Is 50 degrees celsius still ok or not?

Answer: 
Let me suggest a totally different approach:

Why not work **with** the cool conditions instead of against? 

* You could let the dough proof for a long time, e.g. overnight in the fridge. This allows for a lot less yeast and hence a less *yeasty* taste, which is usually desired. Also, more complex flavors develop during long proofing times. (There is a reason french baguette may wait for two days before baking.) For a start, aim for about 5% yeast1 and use cool instead of lukewarm liquid.   

You might have to adjust your attitude, because this requires some planning ahead, but gives you more degrees of freedom on the other hand: Fresh bread / cake in the morning without having to get up before dawn and more tolerance with regard to proofing / timing - the dough can handle an extra hour or two in the fridge easily. (Especially nice if you have a baby or a crazy schedule...)
* You could also dump the dough in cold water and proof it there. As crazy as it sounds, it works. See more [here](https://cooking.stackexchange.com/questions/52124/what-are-the-advantages-of-bathed-bread/52138%2352138).

If you'd rather stick with warm conditions, I'd aim for [30°C](https://www.exploratorium.edu/cooking/bread/yeast_temp.html) for optimum (=quickest) activity. Yeast starts to die at about 45°C, completely dead at 55°C. Also, warmer dough tends to proof unevenly and have a "flat" taste (can't find a better word).

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1 fresh yeast, percentage based on flour weight.

Adjust dry yeast accordingly: fresh to dry conversion rate is 1:3, so use 2% dry yeast.
I use the pull-out warming tray on my oven set on its lowest temperature. I've never actually checked the temperature, but its rather cool. I can easily touch the bottom of the drawer without any discomfort.