In this work, we present the application of the BACKONE, PC-SAFT, SAFT-VR, and soft-SAFT models to examine the impact of the accuracy of representation of third virial coefficients on the behavior of the correspondingly predicted Joule-Thomson inversion curve (JTIC). Calculations were performed for nonassociating fluids such as ethane and pentane, associating fluids such as alcohols, and quadrupolar fluids such as nitrogen and carbon dioxide. By taking advantage of the molecular nature of the models investigated, we were able to evaluate the separate contributions to the Helmholtz free energy. Nonassociating and quadrupolar fluids are mostly governed by the dispersion contribution, whereas, as expected, the association term plays a predominant role for associating compounds. We validated our previous findings that deviations from the correct shape of the JTIC at high temperatures directly reflect the inadequacies in the predicted third virial coefficients. Consequently, much attention should be dedicated to the reliable description of virial coefficients in building and testing any newly developed equation of state.