A microscopic explanation for the experimental observations of the solvation of methane in water is proposed by way of free energy and structural information estimated using computer simulations. In particular, the temperature dependence of both the free energy of solvation as well as structural information is calculated. The free energy is estimated by reweighting histograms from canonical and grand canonical Monte Carlo simulations along a thermodynamic path. The results for the free energy and structural changes are found to be in qualitative agreement with experimental data. We propose that the decrease in entropy found in the solvation process is brought about by excluded volume effects on mixing the two components rather than any local "freezing" of the water around the methane. At the same time the enthalpy of solvation is determined by the solute-solvent interaction. A weak dependence of the hydration free energy with temperature is found. A possible explanation lies with the relatively low temperature sensitivity of the methane-water radial distribution functions.