The present work uses the Levenberg-Marquardt Method (LMM) and a Particle Swarm Optimization (PSO) for estimating the heat generation function for a Guarded Hot-Plate Apparatus (GHPA). This device is used for thermal conductivity determination of insulating materials. The problem is one-dimensional in cylindrical coordinates. Geometries are a disc (Hot-Plate) and an annulus (Guard). A heat generation function is estimated considering one to five parameters. Capability of each method for recovering the analytical function is tested. Results are satisfactory for this kind of problem.