I would be more concerned with the humidity. You can get a temp/humidity meter at a hardware store. Keep the wood where it is the driest. Still, just because I'm ocd, I would not want to spend too much time at full draw with a frozen bow.
Its always humid where I am at. I built a wood/glass case for my bows and staves. Its like a big gun case. Inside is the humidity sensor and a small $12 space heater. With the heater off the meter usually shows 70-80% humidity or even pegs out. On low, the heater will keep the case inside anywhere from 30-50%, and it helps heat the shop.
I regulate it depending on what i am doing. Overall it keeps the moisture down on my wood, but I also regulate it to dry out bows that I just put finish on or maybe hideglue used in backings, stains, paint, whatever. If I'm working a stave to tiller and I question its moisture content I will put it in the case between tiller sessions.
I really like the setup and I highly recommend it.