When x‐ray absorbers such as W are sputtered directly onto x‐ray mask membranes a large temperature gradient is set up due to the power input from the plasma, and the very inefficient thermal conduction in the plane of the thin membrane. To obtain absorber stresses sufficiently low that pattern distortion is negligible, the temperature gradient across the membrane must be no greater than a few degrees. To achieve this we introduce He at about 665 Pa (5 Torr) between the back surface of the membrane and an Al heat sink heated to 200 °C, separated by 1 mm. Uniform stress is easily achieved. The He gas also allows one to implement aninsitustress control feedback system based on an array of optically based gap sensors which can determine stress of the deposited film from the change in the pressure‐induced bulge of the membrane.