The internal temperature environment of a hydrogen maser (H maser) is one of the main factors, which limit the frequency stability of hydrogen atomic clocks (HACs). In the present study, the thermodynamic interactions between the atomic transition frequency and the cavity-bulb assembly affecting the H maser were investigated, and the cavity-pulling effect and the bulb wall frequency shift effect induced by the change in temperature were quantitatively analyzed and calculated. Moreover, the effect of the temperature gradient on the temperature sensitivity of the frequency stability (i.e., the frequency-temperature effect) was qualitatively analyzed. The precision temperature control system was optimized based on the HAC temperature stability requirement through the simulation of the temperature field for different heating pattern methods. The optimization effect was verified experimentally, and the results show that after optimizing the design, the temperature stability is improved from ±0.005 K to ±0.001 K, and the frequency deviation is decreased from 3 × 10-15 to 1 × 10-15. The research results may provide theoretical and practical references for improving the frequency stability and accuracy of HACs.