This paper presents a method developed for determining temperature distribution in a semi-analytical way within tri-dimensional solid-state circuits and packaged devices in steady state conditions. The method is an efficient route to investigate large ranging sized structures with an arbitrary complex layout composed of multiple material layers and localized heat sources. The method, called the Discrete Boundary Resistance (DBR), consists in decomposing the structure into layers of different sizes to develop the temperature solution as a Double Fourier Series after subdividing the contact boundaries into discrete elements. The solution is expressed as a function of thermal resistance attached to the contact boundaries connected to a temperature reference. The performance of the method has been studied in regards with a three-dimensional device involving a non-uniform distribution of voids between layers. Computational time was found to be shorter than ones achieved with the Finite Element method.