Electron transpiration cooling (ETC) is a recently proposed approach to manage the high heating loads experienced at the sharp leading edges of hypersonic vehicles. Computational fluid dynamics can be used to investigate the feasibility of ETC in a hypersonic environment. A modeling approach is presented for ETC, which includes devloping the boundary conditions for electron emission from the surface, accounting for the electric field and space-charge limit effects within the near-wall plasma sheath. Two different analytical models for space-charge limited emission are discussed. The first model assumes that the electrons are emitted cold from the surface while in the second approach the emitted electrons have a finite temperature. The theory shows that emitted electrons with a finite temperature, referred to as warm emission in the present paper, can reach higher levels of emission. This is important because the benefit of ETC, mainly reduction in the surface temperature, is directly correlated to the level of electron emission from the surface. The space-charge limit models are assessed using 1D direct-kinetic plasma sheath simulations. The simulations agree well with the space-charge limit theory proposed by Takamura et al. for emitted electrons with a finite temperature. Both models are implemented into a CFD code, LeMANS, and run for a test case typical of a leading edge radius in a hypersonic flight environment. The CFD results show finite temperature theory results in a larger reduction in wall temperature because more electron emission is allowed for than the cold emission theory. However, even with the electrons being emitted with a finite temperature, the emission still reaches space-charge limits for the test case considered, which can limit the benefits of ETC.