Activation heat capacity is emerging as a crucial factor in enzyme thermoadaptation, as shown by non-Arrhenius behaviour of many natural enzymes1,2. However, its physical origin and relationship to evolution of catalytic activity remain uncertain. Here, we show that directed evolution of a computationally designed Kemp eliminase introduces dynamical changes that give rise to an activation heat capacity absent in the original design3. Extensive molecular dynamics simulations show that evolution results in the closure of solvent exposed loops and better packing of the active site with transition state stabilising residues. Remarkably, these changes give rise to a correlated dynamical network involving the transition state and large parts of the protein. This network tightens the transition state ensemble, which induces an activation heat capacity and thereby nonlinearity in the temperature dependence. Our results have implications for understanding enzyme evolution (e.g. in explaining the role of distal mutations and evolutionary tuning of dynamical responses) and suggest that integrating dynamics with design and evolution will accelerate the development of efficient novel enzymes.