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The authors are currently investigating the use of bulk high temperature superconductors as trapped field magnets (TFMs) in order to increase the electrical and magnetic loading of an axial gap, trapped flux-type superconducting electric machine. In electric machines, the use of superconducting materials can lead to increases in efficiency, as well as power density, which results in reductions in both the size and weight of the machine. In all cases, to trap the maximum possible field Btrap, the magnitude of the applied field needs to be at least Btrap, which invariably requires large magnetizing coils, and which is impractical for most applications of these materials. To simulate the thermal effects of an external field on the trapped field, a thermally-isolated model of a bulk superconductor has been used to simulate its thermal properties. This is carried out using the COMSOL Multiphysics® Heat Transfer Module coupled with the electromagnetic formulation.