A more advanced form of nuclear propulsion known as centrifugal nuclear thermal propulsion (CNTP) promises increased propellant temperatures that could lead to a high specific impulse in the range of 1500 to 1800 s with hydrogen. This design has the potential of opening opportunities to perform missions to destinations much farther than currently possible. However, the CNTP concept poses many engineering challenges due to the nuclear fuel operating at high temperature in a liquid phase. A one-dimensional, steady-state thermal model of the liquid uranium fuel has been constructed to understand the limitations of this concept and the potential design considerations. Three related basic designs are considered, and key design parameters are varied in order to predict the temperature levels and void fractions across the liquid uranium pool.