Nonlinear high-harmonic generation in micro-resonators is a common technique used to extend the operating range of applications such as self-referencing systems and coherent communications in the visible region. However, the generated high-harmonic emissions are subject to a resonance shift with a change in temperature. We present a comprehensive study of the thermal behavior induced phase mismatch that shows this resonance shift can be compensated by a combination of the linear and nonlinear thermo-optics effects. Using this model, we predict and experimentally demonstrate visible third harmonic modes having temperature dependent wavelength shifts between -2.84 pm/degrees C and 2.35 pm/degrees C when pumped at the L-band. Besides providing a new way to achieve athermal operation, this also allows one to measure the thermal coefficients and Q-factor of the visible modes. Through steady state analysis, we have also identified the existence of stable athermal third harmonic generation and experimentally demonstrated orthogonally pumped visible third harmonic modes with a temperature dependent wavelength shift of 0.05 pm/degrees C over a temperature range of 12 degrees C. Our findings promise a configurable and active temperature dependent wavelength shift compensation scheme for highly efficient and precise visible emission generation for potential 2f-3f self-referencing in metrology, biological and chemical sensing applications.