In this work, we use a molecular based equation of state, the Soft-SAFT equation, to predict complete Joule-Thomson inversion curves for carbon dioxide and the n-alkane series, including heavy n-alkanes up to octatetracontane (n-C48H98). Comparisons with available experimental and correlation data, for carbon dioxide and the lighter n-alkanes, show good quantitative agreement. We observe a strong dependence of the inversion curve on the set of molecular parameters used in the calculations, especially near the inversion point and in the high-temperature region. The equation is able to predict the general trend of inversion curves even for extreme conditions, with reduced pressure, P-r = P/P-c, values up to 40, and reduced temperatures, T-r = T/T-c of almost 5.