THERM is a three-dimensional finite-element computer program for solving transient heat conduction problems. This report presents the techniques used to develop THERM. The theory described consists of a governing equation, boundary conditions, and an equivalent variational principle. The matrix equations used in THERM are derived using both vector and tensor analysis. These equations used finite-element approximations for the geometry and a finite-difference approximation for the time. THERM has finite-element formulations using both Cartesian or cylindrical coordinates. Several example problems are included to demonstrate that the THERM formulations are correct and that THERM can be used to solve meaningful problems. 7 refs., 4 figs., 6 tabs.