Silicon-nitride based microcavities are widely used integrated optical devices that are not only capable of outputting optical frequency combs for precision ranging and optical clocks but also serve as efficient on-chip quantum light sources. The stability of optical frequency combs in microcavities is a major condition for the practical application of these devices. In this study, the evolution and thermal self-stability of optical combs in silicon nitride microcavities are theoretically and experimentally investigated. Based on the nonlinear process and thermal dynamics of microcavities, the comb evolution and thermal self-stability of an optical comb in a microcavity under different powers and detuned continuous optical pumping are analyzed. Results show that the output of the “Turing Ring” state can be adjusted by precisely controlling the pump power and by detuning. Moreover, the effects of noise can be compensated by resonance drift caused by power and wavelength disturbance to achieve stable operation. This study provides a critical foundation for experiments based on microcavity quantum sources.