This paper explores the possibilities of cooling a permanently inhabited lunar base with a reverse Brayton cycle Thermal Control System (TCS). Based on an initial stage outpost, the cooling needs are defined. A thermodynamic performance model for the Brayton cycle is derived using ideal gas analysis. This model includes inefficiencies and irreversibilities of the components. The free parameters in the thermodynamic model are successively removed using limiting values for efficiencies and determining operating parameters by suboptimizations. In essence a model for cooling efficiency as a function of rejection temperature alone is obtained. For every component of the system a mass model is applied and the overall mass is determined. The last remaining degree of freedom, the rejection temperature, is eliminated by an optimization for lowest overall mass. The result for minimal TCS mass is compared to a reference TCS using a Rankine cycle. It is found that the Brayton cycle is not competitive with the Rankine TCS.