Leakage of CO2 from a hypothetical geologic storage reservoir along an idealized fault zone has been simulated, including transitions between supercritical, liquid, and gaseous CO2. We find strong non-isothermal effects due to boiling and Joule-Thomson cooling of expanding CO2. Leakage fluxes are limited by limitations in conductive heat transfer to the fault zone. The interplay between multiphase flow and heat transfer effects produces non-monotonic leakage behavior.