An adaptive finite-volume method which maps the time-dependent, curvilinear geometry of annular liquid jets into a unit square is developed to study the fluid dynamics and heat transfer of these jets once combustion within the volume that they enclose ceases. The method employs a strong-conservation law form for the governing equations, upwind and central differences for the convective and diffusive fluxes, respectively, and is conservative and implicit. It is shown that the cooling of annular liquid jets is characterized by thin, thermal boundary layers at the jet's interfaces and rapid pressure and temperature variations initially, whose accurate resolution demands the use of very small time steps and grid sizes. It is also shown that the pressure of the gases enclosed by the jet and The temperature and heat flux at the jet's inner interface drop steeply initially and that the steepness of this drop increases as the Weber number is decreased and as the nozzle exit angle decreases from outwardly to inwardly directed flows. The effects of the initial pressure and temperature, jet's thickness-to-mean radius ratio at the nozzle exit, Froude, Reynolds and thermal Péclet numbers, gas specific heat ratio, and liquid-to-gas specific heat and density ratios on the cooling of annular liquid jets are also analyzed.