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In this paper, we investigate the impact of the granularity of the power distribution for accurately predicting semiconductor chip temperature fields. Specifically, we calculate the transfer functions between power distributions and resulting temperature maps for various microprocessor packages and cooling conditions, which establish a minimum granularity required for accurate thermal analysis. The purpose of this paper is twofold: First, we like to provide some general guidelines for the impact of different power granularities on the global chip temperatures and second we intend to spike a broader discussion about to which extent small heating effects can affect chip temperatures for circuits under full operation. As such this work is not only beneficial for package and cooling solution engineering but is also important to circuit designers and computer architects in their battle against hotspots in microprocessors.