Other things are going on but the above is the simple answer. However, if the dough is heated too much the yeast mold is killed and the dough rises less or not at all. As to how enzymes work. That is a very complicated. Different enzymes work differently.
Dough rises because of production of carbon dioxide, a gas that has no color or taste.
Alternatively, the gas can be produced by enzymes and chemicals. This may sound unattractive, but the production of gas by baking powder is completely harmless. Yeast has a faster metabolism at higher temperatures but would die when it becomes too hot. So by the time your bread is baked it no longer contains alive cells. The chemical processes caused by baking powder are also faster at higher temperatures.