Laser energy absorption and subsequent heat removal from diffraction gratings in chirped pulse compressors poses a significant challenge in high repetition rate, high peak power laser development. In order to understand the average power limitations, we have modeled the time-resolved thermo-mechanical properties of current and advanced diffraction gratings. We have also developed and demonstrated a technique of actively cooling Petawatt scale, gold compressor gratings to operate at 600W of average power - a 15x increase over the highest average power petawatt laser currently in operation. Combining this technique with low absorption multilayer dielectric gratings developed in our group would enable pulse compressors for petawatt peak power lasers operating at average powers well above 40kW.