Numerical simulations are performed to develop a new heat transfer coefficient correlation applicable to the gas cooler design of a trans-critical carbon dioxide air-conditioner. Thermodynamic and transport properties of the supercritical gas cooling process change dramatically and significantly vary heat transfer coefficients to be much different from those of single or two phase flows. In the present study, the elliptic blending second moment turbulent closure precisely reflecting the effects of these thermo-physical property variations on the turbulent heat transfer is employed to model the Reynolds stresses and turbulent heat fluxes in the momentum and energy equations. Computational results related to the development of turbulent heat transfer during in-duct cooling of supercritical carbon dioxide were used to establish a new heat transfer coefficient correlation that would be widely applicable to a gas cooler design involving turbulent heat transfer of supercritical carbon dioxide in square cross-sectional duct flows.