The linear relation observed between heat flux and radiogenic heat production of near-surface rocks in many individual geological provinces of the world can be explained in terms of various source distributions. If this relation survives through differential erosion in space, a unique solution exists under the condition of steady state heat conduction such that heat production decreases exponentially with depth. During an episode of differential erosion in a region with an exponential source distribution, an analytical solution shows that the transient heat flux is no longer linearly related to the heat production of the exposed rocks. Depending upon the rate and duration of erosion as well as the variation of temperature at the ground surface, the transient heat flux may increase, while the near-surface rocks which contain exponentially higher amounts of heat generating elements are stripped away. After the termination of erosion, it takes ~20% of the duration of erosional episode, as shown by a finite element analysis, for the transient heat flux to reach its steady state value. In a tectonically active area, a linear relation may not be observable owing to transient effect of erosion and other perturbing factors.