This paper presents a straight-forward finite element approach for the quantification of electronic package thermal performance under uncertainty. The method makes use of high accuracy sensitivity calculations and a gradient-based minimization method. The approach was applied to the thermal analysis of a ball grid array (BGA) package under uncertainty to illustrate its capabilities. The effect of uncertainty in the heat source, heat transfer coefficient, ambient temperature, and thermal conductivities of the component materials on the probability of exceeding a specified average junction temperature at the die-heat-spreader interface was studied. In addition, the performance and accuracy of two different methods for computing the required sensitivities were compared. Results showed that the average junction temperature probability was more sensitive to some system parameters over others, providing crucial information for selecting the manufacturing tolerance of BGA package components. For parameters identified as especially sensitive, selecting components with tighter tolerances will reduce uncertainty and increase the overall reliability. And for less sensitive parameters, selecting larger tolerance could help reduce manufacturing costs.