Dynamic models are needed to assess controllability of heat exchangers and heat exchanger networks. A simple model is desirable, but all important model features must be included. We discriminate between important and less important model features by order of magnitude argumentation, comparison of controllability measures and dynamic simulations. Important model features for single heat exchangers are model order, wall capacitance and fluid compressibility, whereas how configuration and temperature driving force have only a small effect on the dynamics. The most important model feature for heat exchanger networks is residence time of the connecting pipes. Simpler models may fail to identify inherent control limitations such as zeros in the right half plane.