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've done this a few times, kinda - we have a baking stone, and I'll preheat that, make sure it's cool enough to touch, and set the dough on the warmed stone. 

It works pretty well to give a warm environment, the warmth lasts because the closed oven contains heat, and there's little to no risk of overheating the yeast. I have both gone with regular preheating for ~5min, and the lowest-temperature-preheating for a bit longer, the former is quicker to heat but more likely to overshoot (or needing time to even the heat out), the latter slower and more controlled.

Another *potential* alternative, depending on your oven, might be to turn the oven on (bake setting, usually) but keep the temperature set to zero. In our oven, that turns on the light, the machinery is humming, and the oven gets kinda warm - not hot, but just warm, preparing to heat but not doing so. 

I've used this to dehydrate things before, because I can leave it going for quite some time without needing to re-check or re-warm. It wouldn't work for me with bread dough, since with aforementioned baking stone it would take longer to warm up than it would for the dough to actually rise (since especially the bottom of the dough, against the stone, will rise very differently from the top) . But if you don't have a baking stone it may work very well for you.