We have developed the theoretical model for calculation of the main characteristics of pyroelectric response of pyroactive multilayer structures, which are the basic elements of the modern pyroelectric detectors of radiation and other transducers. In the framework of the proposed model, the dependences of the pyroelectric response frequency spectra on the ferroelectric film thickness have been investigated. It was found that a pronounced extrinsic size effect is inherent to the pyroelectric response frequency spectra, such as the strong thickness dependence of the response maximal value and its frequency position. The thickness dependences of the frequency position of the maximum pyroelectric response and the optimal thickness of the pyroactive ferroelectric film have been calculated. The frequency spectra of the pyroelectric current and voltage calculated theoretically are in quantitative agreement with the experimental ones for the Al/P(VDF-TrFE)/Ti/Si pyroactive structure. The developed procedure is important for improving the sensitivity of pyroelectric devices. The obtained analytical expressions allow optimizing the performances of pyroactive elements using the existence of the size effect, which depends on the pyroactive ferroelectric film and substrate thicknesses, as well as on the conditions of heat transfer and exchange at the corresponding boundaries of the pyroactive structure.