The shape of the Joule-Thomson inversion curve of a fluid at high temperatures is shown to be directly related to its second and third virial coefficients. Experimental values and empirical correlations of the third virial coefficient of carbon dioxide are used to resolve a previously observed conflict between inversion curves obtained from different equations of state for this fluid. In particular, third virial coefficients predicted from the Pitzer-Sterner equation of state are shown to be in error, resulting therefore in an incorrect inversion curve.