The success of the development of nuclear thermal propulsion devices and thermionic space nuclear power generation systems depends on the successful utilization of nuclear fuel materials at temperatures in the range 2000 to 3500 K. Problems associated with the utilization of uranium bearing fuel materials at these very high temperatures while maintaining them in the solid state for the required operating times are addressed. The critical issues addressed include evaporation, melting, reactor neutron spectrum, high temperature chemical stability, fabrication, fission induced swelling, fission product release, high temperature creep, thermal shock resistance, and fuel density, both mass and fissile atom. Candidate fuel materials for this temperature range are based on UO2 or uranium carbides. Evaporation suppression, such as a sealed cladding, is required for either fuel base. Nuclear performance data needed for design are sparse for all candidate fuel forms in this temperature range, especially at the higher temperatures.