Adaptive membrane masks have recently been reported for the correction of distortions in integrated circuit masks and wafers. In these masks radiative heating is selectively applied to portions of the mask membranes. By controlling local heating, dimensional changes are made to the membrane which correct overlay errors between the mask and the wafer. The method is applicable to almost all of the next generation lithographies, and can correct distortions arising from the mask, the wafer, or the exposure tool. In previous work it was assumed that in-plane heat flow through the thin membranes was negligible, and that the local temperature rise was proportional to the heat input. The present work demonstrates that although there is substantial in-plane heat flow, its effects may be accounted for and a very wide range of temperature distributions may be generated on the membrane. These temperature distributions can then be used to correct almost arbitrary distortions. (C) 2004 American Vacuum Society.