We consider a problem arising in designing Compact Thermal Models (CTMs) for the purpose of simulating the thermal response of a package. CTMs are often preferred over more detailed models due to their minimal representation and the reduced computations required to obtain accurate nodal temperature predictions under hypothetical scenarios. The quality of CTM performance depends on the determination of an appropriate set of parameters that drive the model. The subject of this paper is a heuristic nonlinear optimization approach to computing the set of CTM parameters that best predicts the thermal response of a package. Our algorithm solves a series of one-dimensional nonconvex optimization problems to obtain these parameters, exploiting the special structure of the CTM in order to improve both the execution time of the algorithm and the quality of the CTM performance. We conclude the paper by providing a brief array of computational results as a proof of concept, along with several possible future research extensions.