To precisely obtain the viscoelastic parameters of rubber at different temperatures and strain levels, stress relaxation experiments were conducted on Z090 compound at temperatures of 293K, 323K, 353K, and 373K with strain levels of 10%, 30%, 50%, and 70%. The results indicate that the stress relaxation of Z090 compound exhibits a distinct nonlinear relationship with both temperature and strain. Based on the stress relaxation data of Z090 rubber compound at different strain levels under temperatures of 293K, 323K, and 353K, the Parallel Rheological Framework (PRF) constitutive model was first introduced to characterize the nonlinear relationship between stress and strain. Then, temperature-explicit parameter expressions of the PRF model were constructed to describe the effect of temperature. Finally, a modified PRF model capable of simultaneously depicting the nonlinear influences of both temperature and strain was established. Using this modified PRF model, the stress relaxation behavior of Z090 compound at 373K was predicted and compared with experimental results, demonstrating excellent predictive performance. Thermal-mechanical coupling simulations were conducted using the modified PRF model on dumbbell-shaped cylindrical specimens. The obtained temperature distributions aligned with experimental trends, demonstrating the model's effectiveness for simulating dynamic heat generation in rubber structures under complex operating conditions.