Every child knows that heating melts things, and that keeping them cool keeps them solid. That’s why car engines and computer chips must be cooled and why we’re not about to explore the surface of the Sun anytime soon. The reasoning is simple: at high temperature, the free energy  F=E−TS is minimized by maximizing entropy, so disorder becomes favorable and order melts away. In this talk, I will present models that exhibit the opposite behavior: systems that freeze at arbitrarily high temperatures, defying the standard thermodynamic argument.