An analytical three-dimensional transient temperature solution of a two-layer semi-infinite plate structure with embedded heat sources is discussed. The thickness of the second layer is assumed to extend to infinity. By incorporating the method of images this solution can be used to approximate the structure with finite second-layer thickness. Exact temperature can also be obtained for the rectangular lateral boundaries by the use of the method of images. The correct derivation of the solution is verified by comparing it with the result of the steady-state temperature solution. A computer program has been written based upon the solution and the method of images. A variety of device structures have been studied. Results on the thermal risetime and the effect of the second-layer medium have been obtained. The software is particularly useful for devices operating under pulsed or switching conditions.<<ETX>>