In this review we discuss the development of methodology for calculating the temperature dependence and thermodynamic activation parameters for chemical reactions in solution and in enzymes, from computer simulations. We outline how this is done by combining the empirical valence bond method with molecular dynamics free energy simulations. In favorable cases it turns out that such simulations can even capture temperature optima for the catalytic rate. The approach turns out be very useful both for addressing questions regarding the roles of enthalpic and entropic effects in specific enzymes and also for attacking evolutionary problems regarding enzyme adaptation to different temperature regimes. In the latter case, we focus on cold-adaptation of enzymes from psychrophilic species and show how computer simulations have revealed the basic mechanisms behind such adaptation. Understanding these mechanisms also opens up the possibility of designing the temperature dependence, and we highlight a recent example of this.