Droplet evaporation within combustion chambers is of high importance for stable and efficient combustion. For ambient pressures exceeding the critical pressure of the injected fuel, evaporation processes are not fully understood yet. Especially the temperature evolution of the injected fuel is a key parameter to understand the transition of near critical droplet evaporation to dense fluid mixing. Hence, this study shows various approaches to investigate the temperature evolution of alkane droplets in a nitrogen atmosphere under high temperature and pressure conditions. First, we present a direct numerical simulation of a levitated alkane droplet and compare it with two different analytical evaporation models. The latter are the non-equilibrium models by Gyamarthy as well as Young. The simulation of a levitated droplet is performed with the multiphase solver FS3D. For that, the implemented evaporation models are adapted and extended to account for stable simulations in high pressure and temperature regimes. Based on these insights the vapour concentration in the wake of a free falling droplet is investigated with FS3D and collated with experimental Raman scattering results. Finally, the temperature profile gained from the direct numerical simulation in the wake of the free falling droplet is compared to a re-evaluation of the Raman scattering results. This re-evaluation is based on the PC-SAFT equation of state and an adiabatic mixing assumption.