Recent development in coating deposition processes for aluminum mirrors that are protected with a metal-fluoride overcoat (such as LiF, MgF2, or LiF) have improved reflectance performance particularly in the far-ultraviolet (FUV) part of the optical spectrum. The active research in this area is motivated by the fact that these gains in reflectance are expected to significantly increase the throughput of any future FUV-sensitive NASA missions into the Lyman Ultraviolet. These reflectance improvements are attributed, in part, by performing the metal-fluoride overcoat depositions with the substrates at an elevated temperature as high as 220-250 degrees Celsius. ZERODUR® is a widely used material as a mirror substrate because, among other things, it exhibits a low coefficient of thermal expansion (CTE) over a wide range of temperatures. Moreover, ZERODUR® has recently been proposed for several future NASA concept missions where this improved FUV mirror coating may be used. Given the elevated temperature at which these improved FUV coatings are produced, it is imperative to make sure that heating of the substrate will not significantly impact the final figure of the coated mirror. In this paper, we will study and report the effects of heating ZERODUR® up to the highest temperature mentioned above (250 degrees Celsius) during a simulated coating process. These studies are relevant since it has been reported the CTE will change slightly if ZERODUR® is cooled down from application temperatures between 130 degrees Celsius and 320 degrees Celsius with rates that differ from the initial production annealing rate of 3 degrees Celsius per hour.