A turbomachine includes a compressor configured to compress air received at an intake portion to form a compressed airflow that exits into an outlet portion. A combustor is operably connected with the compressor, and receives the compressed airflow. A turbine is operably connected with the combustor, and receives the combustion gas flow. The turbine has a plurality of wheels and a plurality of buckets. The turbine receives compressor bleed off air to cool the wheels and buckets. A cooling system is operatively connected to the turbine. The cooling system includes a plurality of heat pipes located axially upstream of at least one of the wheels. The heat pipes are operatively connected to a bearing cooler system. The heat pipes and the bearing cooler system are configured to transfer heat from the compressor bleed off air to one or more heat exchangers.