This work details a computer-based modeling tool for predicting temperatures in three-dimensional multilayer microelectronic packages. It is capable of modeling surface connections (e.g., wire bonds and pins), edge connections (e.g., leads), and thermal vias. A three-dimensional control-volume finite difference method is used, permitting transient as well as steady solutions. Numerical behavior is examined with respect to the device geometry and external environment. The features of this tool are demonstrated on a sample multilayer package. The effects of the modeling scheme are discussed. An alternate version of the program removes a layer from the numerical model to simplify the solution of the problem. To compensate for the removal of the layer a contact resistance is added. This replaces the thermal resistance the removed layer provided in the z-direction. The x-y conductivity of the adjacent layers are modified based on the removed layer thickness and conductivity. This measure imitates the spreading resistance or conductance that the removed layer provided. The effect of removing a layer in the model is studied, documenting the relationship between layer thickness and conductivity and the error introduced by removing the layer. A simple relationship is sought which can indicate the instances in which the computer model can be simplified. The results are applicable to any method including finite element and series-analytical methods. / Master of Science