A method is provided of reducing lockout time of a gas turbine engine which includes: an inlet, a compressor, a combustor, a turbine, and an exhaust duct, where the compressor and the turbine are carried on a turbomachinery rotor and each include an array of blades mounted for rotation inside a casing of the engine. The method includes: operating the engine at a first power output; shutting down operation of the engine without substantially reducing the power output beforehand, wherein thermomechanical changes occur in the engine subsequent to shutdown that tend to reduce a radial clearance between at least one of the blades and the casing; and subsequent to shutting down the engine, (1) heating the casing and/or (2) pumping an airflow of ambient air into the inlet and through the casing, past the rotor, and out the exhaust duct, so as to reverse at least partially the thermomechanical changes.