Thermal detectors which convert the incident radiation to heat are frequently used to give a periodic response to the external signal modulated at a fixed low-frequency chopping frequency. Many workers have ascertained the bolometric response of high-quality epitaxial superconducting films on different substrates to chopped laser radiation. Based on these observations we made an a priori assumption that the voltage response of thin film is entirely due to a thermal mechanism, i.e. in the proposed one-dimensional heat conduction analysis any possible non-equilibrium processes are neglected. A new analytical formula is derived for the mean temperature increase in the superconducting film. This formula generalizes the previously well known analytical approximations. Further we explore a specific numerical example based on experimental data for the optical response of a thin () high- Bi-based film on an substrate irradiated by chopped He - Ne laser radiation ( nm). On the basis of the theory and the chopping frequency dependence of the peak voltage response an implementation of a new diagnostic method for evaluation of the thermal Kapitza conductance at the superconducting film - insulator interface is demonstrated.