Image placement accuracy is a limiting factor for all of the next generation lithographies (NGLs). Previous work has shown that thermally induced displacements can improve image placement in membrane masks, compensating errors on the mask as well as errors already printed on the wafer. Consequently, such "adaptive" masks may find applications even in NGLs that do not presently use membrane masks. We have modeled the thermal distributions needed to compensate arbitrary mask distortions both for full-field and scanned exposures. For full field, the membrane is divided into an array of individual heating zones. We find that a 6 x 6 array is adequate to minimize many slowly varying distortions, and that even better results are obtained with a 12 x 12 array. The computation for the 6 x 6 array takes a few seconds on a personal computer. For a scanned exposure, e.g., an x-ray beam on a storage ring, only the line being exposed must be corrected at any given time. This minimizes the heat load on the mask, as well as permitting a simple Fourier analysis. Detailed procedures for both methods of correction are presented.