The idea of correcting x-ray mask distortion through differential heating of the membrane (i.e., projecting a heat pattern onto the membrane that introduces a correcting distortion which cancels the original undesired distortion) was first proposed by Feldman [J. Vac. Sci. Technol. B 17, 3407 (1999)]. Because this correction strategy relies on a precise heat pattern. one must account for how thermal diffusion would blur the edges of the pattern. Here, we numerically analyze how thermal diffusion affects this correction strategy and find that no compensation is necessary if the blurred regions are smaller than the spatial frequency of the distortion correction. We also devise compensation techniques to correct for the temperature distribution effects of thermal diffusion. Our results show how one might construct a real-time correction of arbitrary in-plane distortion through local heating.