I agree with Murray (how can I do otherwise?). Dry is far more dangerous than heat.

A case does protect the instrument from fluctuations in temperature/humidity. That is, it takes a period of time for a condition to change in the case. If you live in an area in which the inside is dry for long periods of time, eventually the dry air will damage the instrument in its case.

In some tropical conditions, where it is really humid, a form of fungus can grow on the finish of the guitar which tends to etch it. The funny thing is that the fungus seems more ready to grow on glossy finished surfaces than on matt.

Murray