In high-frequency power transformers, magnetic material properties cannot be assumed to be constant. These properties vary with frequency, temperature, and magnetic flux density. Heat generation is, in turn, a function of the magnetic permeability, magnetic flux density, and frequency. Current design methods are either empirical or based on linear, uncoupled models. To better understand the relationship between heat transfer, magnetic flux density, material properties, and core geometry in a miniature, high-frequency transformer, a finite-element program has been developed to solve the coupled thermal-magnetic equations for an axisymmetric transformer. The program accounts for nonlinear temperature and magnetic field dependent material properties, geometry, and driving frequency. The program, HT-MAG, is based on a series of derived magnetic field equations. The Ritz method is applied to the magnetic and thermal equations in the development of the program. The program alternately solves the finite element approximations to the thermal and magnetic governing equations until the magnetic properties match within a specified fraction or a maximum number of iterations are performed. In addition, the program can be linked with existing pre- and post-processors or can accept manual pre- and post-processing. Six test cases were run to test the validity of the program. The first two cases tested the uncoupled heat transfer calculations. One of these tested the thermal conduction calculations while the other tested the heat generation calculations. The next two cases tested the uncoupled magnetic equations. The first was a direct current (DC) case, while the second was an alternating current (AC) case. The final two cases tested the thermal magnetic coupling. Solutions to these cases are presented and discussed. / Master of Science