We present the results of an experimental study of the dynamics of thermal self-oscillations of a normal zone in thin films of high-temperature superconductors (HTSC) connected to an external circuit with an inductance and cooled by boiling nitrogen. The response of the system to a harmonic driving force has been studied. Spectral and dynamical characteristics of various oscillative regimes have been determined. It is shown there arises a state of a deterministic chaos in some range of driving frequencies and amplitudes. An effective of synchronization of periodic self-oscillations of a normal zone and thermo-hydrodynamical oscillations caused by the boiling of liquid nitrogen near a film surface has been recognized.