One of the key objectives of the CFAR (compact fusion advanced Rankine) cycle concept for advanced tokamak reactors is to reduce the capital costs of the power conversion system and the balance of plant. A design of the heat rejection system has been done as part of a preliminary cost study in order to evaluate the capital costs of this fusion power plant concept. This system has been optimized to yield the minimum capital cost subject to constraints on the size of the desuperheater/condenser heat exchangers, the pressure drops and the pumping power required for the heat-rejection coolant. The results of this study including estimates of the cost of electricity for the CFAR concept with and without a bottoming plant are reported.