A turbomachine includes a compressor having an inter-stage gap between adjacent rows of rotor blades and stator vanes. A combustor is connected to the compressor, and a turbine is connected to the combustor. An intercooler is operatively connected to the compressor, and includes a first plurality of heat pipes that extend into the inter-stage gap. The first plurality of heat pipes are operatively connected to a first manifold, and the heat pipes and the first manifold are configured to transfer heat from the compressed airflow from the compressor to heat exchangers. A cooling system is operatively connected to the turbine, and includes a second plurality of heat pipes located in the turbine nozzles. The second plurality of heat pipes are operatively connected to a second manifold, and the heat pipes and the second manifold are configured to transfer heat from the turbine nozzles to the heat exchangers.