We develop an analytic model to describe the dynamic average thermal distortion and phase difference between the two principal polarizations in side-pumped Nd:YAG and Nd:glass heat capacity rod lasers. It can be predicted that the average thermal distortion is proportional to the temperature profile on the cross section from the analytic expression and, therefore, it is feasible to measure the temperature profile by wavefront sensing. In addition, temperature-dependent variation of the refractive index constitutes the major contribution of the thermal lensing for Nd:YAG rod lasers. Temperature- and stress-dependent variation of the refractive index constitute the major contributions of the thermal lensing for Nd:glass rod lasers. In the case of the same pumping and cooling conditions, there are the same orders of depolarization loss for Nd-doped YAG, LG-680, LG-750, LG-760, and LG-770 glass rod lasers.