Not allot. Kind of.
You will notice the bow will perform differently dependent on temperature and humidity. The temperature difference will not be so much that it will really effect the bow to a dangerous extent. The worst effects on bows comes from change in temperature. I.e. if you quickly take a bow from a warm place to a cold place without letting it adjust it can cause problems, mostly to do with different bits expanding/contracting at different rates. This can cause problems with modern bows (mostly screwing up your tune rather than damage). Better to let a bow stay at the working temp or at least give it a gentle warm up before shooting.
My biggest worry would be humidity. I would worry a trad composite bow would not perform well in high humidity. Water could get in between the laminates and cause all sorts of problems. I have no evidence of this, but it would be something I would avoid.