We report the results of a theoretical study of the combined end-side pumped solar lasers to solve the problem associated with a recent experimental finding where the unexpected underperformance of the Ce doped Nd:YAG lasers in comparison to pure Nd:YAG lasers was observed. For this, we have developed a theoretical model based on space-dependent rate equations, which considers the effect of the thermal population of the laser levels on the laser output. It is shown that the main reason for the lower laser performance of recently experimentally realized Ce:Nd:YAG solar laser in the end-pumped regime and the fracture of the Ce:Nd:YAG rod at the process is the excessively high thermal load on the end of the laser rod. As a result of our study, we propose easily-feasible solutions based on optimal pumping and cooling configurations. The results of this study also demonstrate that under the necessary conditions, using Ce:Nd:YAG as an alternative to Nd:YAG in the combined end-side pumping configuration could increase the laser output by more than 1.5 times.