Two major parts of the design study for a cold source for the cold neutron beam facility under construction at the Cornell University 500-kW TRIG A reactor are presented. The reasons are discussed for choosing mesitylene as the cold moderator and for choosing conduction through copper rods between the source and a cryogenic refrigerator as the cooling method, the basic criteria for these choices being safety and simplicity of operation. Measurements of the neutron fluxes and nuclear heating rates at the proposed source location are reported. A description is provided of studies to optimize the size and shape of the cold source within the restrictions imposed by the limited available volume, the measured radiation levels, and the chosen materials using Monte Carlo simulation with a personal computer. It is concluded that mesitylene cooled by conduction through copper can provide a very satisfactory, safe, and simple cold source for an intermediate-power research reactor.