The present paper addresses the modelling of fuel injection at conditions of high pressure and temperature which occur in a variety of internal combustion engines such as liquid fuel rocket engines, gas turbines, and modern diesel engines. For this investigation a cryogenic nitrogen jet ranging from transcritical to supercritical conditions injected into a chamber at supercritical conditions was modelled. Previously a variable density approach, originally conceived for gaseous turbulent isothermal jets, imploying the Favre averaged Navier-Stokes equations together with a “k-ε” turbulence model, and using Amagats law for the determination of density was applied. This approach allows a good agreement with experiments mainly at supercritical injection conditions. However, some departure from experimental data was found at transcritical injection conditions. The present approach adds real fluid thermodynamics to the previous approach, and the effects of heat transfer. The results still show some disagreement at supercritical conditions mainly in the determination of the potential core length but significantly improve the prediction of the jet spreading angle at transcritical injection conditions.