We report a heat dynamics analysis of the electrocaloric effect (ECE) in commercial multilayer capacitors based on BaTiO₃ dielectric, a promising candidate for applications as a solid state cooling device. Direct measurements of the time evolution of the sample's temperature changes under different applied voltages allow us to decouple the contributions from Joule heating and from the ECE. Heat balance equations were used to model the thermal coupling between different parts of the system. Fingerprints of Joule heating and the ECE could be resolved at different time scales. We argue that Joule heating and the thermal coupling of the device to the environment must be carefully taken in to account in future developments of refrigeration technologies employing the ECE.