A solar cell concentrator system is offered to satisfy the energy requirement of the satellites orbited around the Earth. The solar cells coupled to the system are exposed to sunlight concentrated 124 times with a Cassegrain type reflector system. To dissipate the waste heat to the space, the cells are bonded on a radiating plate. To calculate the temperature distribution on the surface of the radiating plate, a new FAS (Full Approximation Scheme) solver is developed. This new FAS solver is validated with the Newton method. Additionally, the FAS solver is shown to be 92 times more efficient computationally than the Newton method. Afterwards, radiating plate efficiencies are calculated. These efficiency figures change between 0.1 and 0.02 for different cell temperatures. Next, an energy balance equation is constructed in order to calculate the theoretical operating temperatures of the solar cells. Using energy balance equation and the FAS solver iteratively, solar cell operating temperatures are calculated successfully for different radiating plate thicknesses and solar cell conversion efficiencies. Solar cell operating temperatures are found between 500 K and 1000 K. The present study points out that concentrator systems require highly efficient solar cells operating in the very high temperatures. For instance, in order to operate the cell temperature at 750 K for a 3 mm radiating plate thickness, the cell conversion efficiency should be 70%. Ongoing projects which aim to develop solar cells capable of operating in high intensity-high temperature environments are believed to make it possible to embed solar cell concentrator systems on the next generation satellites.