Methods are disclosed for reducing effects of thermal expansion of a sensitive substrate arising during microlithographic exposure of the substrate using a charged particle beam. Thermal expansion ordinarily causes lateral shift of exposure position of dies (chips) on the substrate which tends to reduce the positional accuracy with which images of the dies are formed on the substrate. Generally, regions of the substrate where entire dies are formed are exposed first, followed by regions (especially peripheral regions) exposed with only portions of dies. In addition, the substrate can be mounted on a wafer chuck configured to circulate a heat-transfer gas in contact with the substrate to remove heat from the substrate. In addition, the wafer chuck can be maintained at a constant temperature by circulating a liquid coolant through a conduit in the body of the wafer chuck.