A gas turbine engine may include a deep heat recovery system, such as a deep heat recovery super critical carbon dioxide (sCO2) system. The deep heat recovery system may include two-stage cooling of the working fluid (such as carbon dioxide—CO2) where at least one of cooling stages is recuperative by transferring heat from the working fluid to a flow of compressed air being supplied to a combustor included in the gas turbine engine. The deep heat recovery system may operate in a supercritical cycle, or in a transcritical cycle depending on the temperature to which the working fluid is cooled during a second stage of the two-stage cooling. The second stage of the two-stage cooling includes working fluid-to-air heat rejection where the air is ambient air.