A temperature management system for a turbomachine, the turbomachine comprising: a compressor including an intake portion and an outlet portion, the compressor having a plurality of rotor blades and a plurality of stator vanes, and an inter-stage gap exists between adjacent rows of rotor blades and stator vanes, the compressor compressing air received at the intake portion to form a compressed airflow that exits into the outlet portion; a combustor operably connected with the compressor, the combustor receiving the compressed airflow; and a turbine operably connected with the combustor, the turbine receiving combustion gas flow from the combustor, the turbine having a plurality of turbine blades, a plurality of wheels and a plurality of nozzles, and a turbine casing forming an outer shell of the turbine; the temperature management system comprising: an intercooler configured to be operatively connected to the compressor, the intercooler including a first plurality of heat pipes that extend into the inter-stage gap, the first plurality of heat pipes operatively connected to a first manifold, the first plurality of heat pipes and the first manifold are configured to transfer heat from the compressed airflow to one or more heat exchangers; and a cooling system operatively connected to the turbine, the cooling system including a second plurality of heat pipes located in at least a portion of the plurality of nozzles, the second plurality of heat pipes operatively connected to a second manifold, the second plurality of heat pipes and the second manifold are configured to transfer heat from the plurality of nozzles to the one or more heat exchangers. a compressor including an intake portion and an outlet portion, the compressor having a plurality of rotor blades and a plurality of stator vanes, and an inter-stage gap exists between adjacent rows of rotor blades and stator vanes, the compressor compressing air received at the intake portion to form a compressed airflow that exits into the outlet portion; a combustor operably connected with the compressor, the combustor receiving the compressed airflow; and a turbine operably connected with the combustor, the turbine receiving combustion gas flow from the combustor, the turbine having a plurality of turbine blades, a plurality of wheels and a plurality of nozzles, and a turbine casing forming an outer shell of the turbine; the temperature management system comprising: an intercooler configured to be operatively connected to the compressor, the intercooler including a first plurality of heat pipes that extend into the inter-stage gap, the first plurality of heat pipes operatively connected to a first manifold, the first plurality of heat pipes and the first manifold are configured to transfer heat from the compressed airflow to one or more heat exchangers; and a cooling system operatively connected to the turbine, the cooling system including a second plurality of heat pipes located in at least a portion of the plurality of nozzles, the second plurality of heat pipes operatively connected to a second manifold, the second plurality of heat pipes and the second manifold are configured to transfer heat from the plurality of nozzles to the one or more heat exchangers. an intercooler configured to be operatively connected to the compressor, the intercooler including a first plurality of heat pipes that extend into the inter-stage gap, the first plurality of heat pipes operatively connected to a first manifold, the first plurality of heat pipes and the first manifold are configured to transfer heat from the compressed airflow to one or more heat exchangers; and a cooling system operatively connected to the turbine, the cooling system including a second plurality of heat pipes located in at least a portion of the plurality of nozzles, the second plurality of heat pipes operatively connected to a second manifold, the second plurality of heat pipes and the second manifold are configured to transfer heat from the plurality of nozzles to the one or more heat exchangers.