A gas turbine engine includes an engine core with a combustor; a turbine including turbine blades; a compressor as a source of cooling air for the turbine blades; and an inducer to accelerate and direct the cooling air onto the turbine blades, and a modulating valve to allow or block cooling air flow into a subset of airflow passageways of the inducer; and a fuel management system to provide fuel to the combustor. The fuel management system includes a primary fuel-oil heat exchanger and a secondary fuel-oil heat exchanger through which oil and the fuel flow, to transfer heat between the oil and the fuel. A method of operating the engine includes using the modulating valve to adjust the cooling air flow based on turbine inlet temperature; and transferring 200-600 kJ/m3 of heat to the fuel from the oil in the primary fuel-oil heat exchanger at cruise conditions.