Under conditions of failure of the emergency core cooling system in a heavy-water production reactor, core melt-down may occur and molten fuel may come into contact with the bottom head of the reactor vessel. A computer code, ACCORD, that features the use of a directional effective thermal conductivity in modeling natural convection in heat-generating liquid pools and the use of a mass transfer coefficient in modeling dissolution of the interior surface of a reactor bottom head into a melt pool has been developed to track the thermal behavior of a melt pool formed inside the bottom head of a reactor vessel and to study the interactions between the melt pool and the bottom head. The discretization scheme for the melt pool is designed specifically for liquid pools bounded from below by curved surfaces. Heat transfer in the melt pool is treated as axisymmetric and two-dimensional while that in the bottom head is treated as locally one-dimensional. The temperature distribution in the melt pool and in the bottom head are solved sequentially instead of simultaneously and are coupled through boundary conditions at the interface between the melt pool and the bottom head. The basic equations and their solution method for the ACCORD code are described. The capability of the code is demonstrated with sample calculations.