Concentration of solar radiation onto the surface of triple-junction solar cells causes high cell temperature and system failure. Recently, several cooling methods were proposed for these systems. However, quantitative evaluation of the essential heat transfer coefficients to maintain stable operation of these systems at different meteorological and operating conditions is not found in the literature. Therefore, in this study, a comprehensive three-dimensional coupled thermal and structural model is proposed for the latest triple-junction AZUR SPACE solar cell. The model is used to investigate the performance of an HCPV system under different solar concentration ratios (CRs), ambient temperature, direct solar irradiance, wind speed, backside heat transfer coefficient, and copper-II substrate area ratios. In addition, a new structure of the solar cell is proposed by modifying the typical solar cell assembly by changing the area of the rear copper layer. The results indicate that by increasing the ambient temperature, CR and direct solar irradiance significantly increase the predicted cell temperature at the same backside heat transfer coefficient. In addition, increasing copper-II substrate area ratios significantly reduces the average cell temperature at the same backside heat transfer coefficient and CR. At the highest backside heat transfer coefficient, when the copper-II substrate area increased, the cell temperature decreased to a certain limit and subsequently remained constant. Critical values of the highest backside heat transfer coefficient were about 200, 600, 1000, and 1600 W/m2 K at CRs of 50, 500, 1000, and 1500 Suns, respectively. In addition, at the highest backside heat transfer coefficient of 1600 W/m2 K, the critical area ratio values were about 2, 3, 4, and 6 at CRs of 50, 500, 1000, and 1500 Suns, respectively.