We present a thermal model to describe the interaction between the visible modes in micro-ring resonators from the third harmonic generation (THG) nonlinear process. We demonstrate that the model can predict the thermal characteristics of the orthogonal THG modes from the interaction and of the resonance coupling between them in micro-ring resonators having a strong nonlinear thermo-optic coefficient. Furthermore, the model can be used to extract the THG efficiency, the linear and nonlinear thermo-optic coefficients and the polarization dependency of the THG modes from the measurement data.