This paper presents an approach to the analysis of transient thermal states in electronic circuits using an analytical solution of the heat equation. Fully three-dimensional analytical time dependent solutions are determined for multilayered structures with the help of Green`s functions (GFs). The GFs required for the solution are found using a Galerkin-based integral method. The entire solution method is illustrated in detail using a practical example, where the results of transient thermal simulations of a real hybrid power module are compared with infrared measurements.