We present simulation of the Joule-Thomson inversion curve (JTIC) for carbon dioxide using two different approaches based on Monte Carlo (MC) simulations in the isothermal-isobaric ensemble. We model carbon dioxide using a two-center Lennard-Jones (LJ) plus point quadrupole moment (2CLJQ) potential. We show that a precision of four significant figures in ensemble averages of thermodynamic quantities of interest is needed to obtain accurately the MC. The agreement between the experimental data, Wagner equation of state (EOS) and our simulations results indicates that the 2CLJQ potential represents an excellent balance between simplicity and accuracy in modeling of carbon dioxide. Additionally, we calculate the JTIC using the BACKONE EOS (that uses the same intermolecular potential as in our simulations) and show that the BACKONE EOS performs very well in predicting the JTIC for carbon dioxide.