This work describes the development of a fully implicit general thermal model (ISCOM) for simulating in situ combustion or steam processes. The model includes 4 phases, a variable number of oil components, a variable number of chemical reactions, gravity and capillary pressure terms, and the possibility of modeling emulsions. The finite-difference formulation of ISCOM operates in one, 2 or 3 dimensions and contains implicit and sequential implicit solution techniques as options. It is highly stable, averaging 30% saturation or molar fraction changes during each time step. The model includes the use of pseudo-phase equilibrium ratios which allows a single formulation, even though phases may disappear. The computer program was designed to emphasize clarity and to optimize storage. Results are presented showing the sensitivity to changes in number of grid blocks and time-step size and showing the influence of harmonic weighting on the grid orientation effect.