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A theoretical method is developed for computing steady heat power in short-circuited heat conducting rods or composite slabs. The method is exact, direct, and computationally most efficient: the construction and sequencing of finer grid point meshes is not required, nor temperature distribution computations of any sort, nor the computation of thermal gradients along some boundary or interface. This new method facilitates several practical objectives, which are carried out and presented in a forthcoming paper [1]. These objectives include both the development of guidelines for using the approximate heat power solution obtained previously in [2,3], and an extensive parameter analysis, which considerably enhances understanding of short circuit phenomena. This improved understanding facilitates the possibility of optimally designing a rod for maximum or minimum heat transmission capability.