Evaporative cooling is an attractive mechanism for heat removal in polymerization reactors where fast, exothermic reactions and high viscosities complicate other means of heat removal. In this work we consider the effect that the mechanism has on the dynamics of a well mixed tank reactor for solution free-radical polymerization of styrene. Continuation and stability analysis reveals the existence of isola structures and oscillatory behavior at typical industrial conditions as well as strong coupling of the degree of evaporative cooling with important parameters like residence time, feed initiator concentration, jacket temperature, and reactor size. Further analysis is performed to try to understand the impact that this behavior has on practical aspects such as reactor design, scale-up, and operation.