Cooling a turbine exhaust case (TEC) employed in an industrial gas turbine engine includes supplying cooling airflow from an outer diameter (OD) to an inner diameter (ID) cavity, supplying a secondary airflow having a pressure greater than the pressure of the cooling airflow to the ID cavity for mixing with the cooling airflow to provide a mixed airflow, and directing the mixed airflow in a serpentine cooling path that includes first directing the mixed airflow radially outward via hollow struts to an OD cavity, then radially inward via hollow fairings that surround the hollow struts.