[en] Design analyses using finite element methods are presented for thermal distortion of water-cooled diffraction grating substrates for a potential application at the LBL Advanced Light Source, demonstrating that refinements in cooling channel configuration and heat flux distribution can significantly reduce optical surface distortion with high heat loads. Using an existing grating substrate design, sensitivity of tangential slope errors due to thermal distortion is evaluated for a variety of thermal boundary conditions, including coolant flow rate and heat transfer film coefficients, surface illumination area and heat distribution profile, and location of the convection cooling surfaces adjacent to the heated region. 1 ref., 5 figs., 2 tabs