Super band-gap time-resolved photoluminescence is employed to measure the transport properties of degenerate election-hole gas in thin GaAs epilayers. It is found that the luminescence decay at wavelengths shorter then the energy gap wavelength is much faster then expected from a simple diffusion-reabsorption model. The results are explained by using a transport model based on Fermi-Dirac carrier statistics and nonparabolic band structure. We have found that only by introducing the above two phenomena the photoluminescence spectra at all energies can be fitted. The importance of the results in studies of hot carrier energy loss rates is discussed.