Why Killing With Heat Works
The reason that this works is simply that they cannot live at extreme temperatures. At 70°F, they will live and even flourish. They will lay eggs and spread. When the temperature gets up near 140°F though, they cannot survive.
They will either have to flee your home, if they can find a way out, or they will die. It is as simple as that. There is no way that they can experience such high heat for such an extended period of time and live.