This is a plausible story, but that doesn't mean it's true. Anecdotally I felt more productive living in a warmer place than when living in Scandinavia. I think it completely depends on your situation and an actual study is needed to prove it one way or the other.

I also recall Jared Diamond debunking this as a theory for why "the west" got ahead in his book Guns, Germs, and Steel.