Well after all I didn't get anyone to join this experiment but at least I got my own results and I think it's about time to share them. I've kept some statistics but since I'm still pretty new to lucid dreaming my dream quality and all other aspects constantly improve, making it hard to come up with some graphical yet correct result.
However I can now support my first claim, at least for myself, I have better sleep and better dreams the colder it is in my room. I still have the theory there are different types of people who dream better if it is cold, while some other need it hot. My recommendation is to observe how good you sleep with different temperature if you seek to improve your dreaming a bit.
Just recently I had 2 lucids in 3 days and it was pretty darn cold in my room, taking me over half an hour just to get comfortable in bed, yet letting me have an awesome night in turn. I will also keep monitoring my sleep behavior under different temperatures, so I might make another update sometime soon, likely around summer.