The isothermal-isobaric Monte Carlo simulation technique was employed to study the behavior of the residual heat capacity of compressed supercritical methanol described by OPLS potential (optimized potential for liquid simulation), as a function of temperature. The main goal was to elucidate the experimentally observed maximum of the heat capacity of some sterically hindered alcohols. The pressure was set to 50 MPa in order to avoid phase transition, and NPT Monte Carlo simulations were performed from 300 K up to 650 K. The calculated residual heat capacity and enthalpy were fitted to the two-state association model (TSAM) equation developed by Cerdeirina et al., and a maximum is found close to the prediction of the TSAM equation. Analysis of the contributions for the heat capacity revealed that the maximum can be attributed to the unlike rates of change of the Lennard-Jones and the electrostatic contributions and their correlation with temperature.