A gas turbine engine comprising; a main compressor section having a high pressure compressor with a downstream discharge, and more upstream locations; a turbine section having a high pressure turbine; a cooling compressor (114; 150) drivingly connected with at least one rotor in the main compressor section, and a source of pressurized air connected to be selectively sent to the cooling compressor (114; 150), to drive a rotor of the cooling compressor (114; 150) to rotate to in turn drive the at least one rotor of the main compressor section at start-up of the gas turbine engine; characterized by further comprising: a heat exchanger; a tap configured to tap air from at least one of the more upstream locations in the compressor section, pass the tapped air through the heat exchanger and then to the cooling compressor (114; 150), the cooling compressor (114; 150) configured to compress air downstream of the heat exchanger, and to deliver air into the high pressure turbine; a cooling compressor valve movable between two positions, with a first position delivering air from the cooling compressor (114; 150) to a line heading to the high pressure turbine, and in a second position delivering pressurized air from the source to the rotor of the cooling compressor (114; 150); a precooler; and a precooler valve movable between two positions, with a first position allowing air from the precooler to move downstream through a part to an aircraft to which, in use, the gas turbine engine is mounted, and in a second position, blocking flow from the precooler to the aircraft, and allowing pressurized air from the source to pass through a conduit to the cooling compressor valve. a main compressor section having a high pressure compressor with a downstream discharge, and more upstream locations; a turbine section having a high pressure turbine; a cooling compressor (114; 150) drivingly connected with at least one rotor in the main compressor section, and a source of pressurized air connected to be selectively sent to the cooling compressor (114; 150), to drive a rotor of the cooling compressor (114; 150) to rotate to in turn drive the at least one rotor of the main compressor section at start-up of the gas turbine engine; characterized by further comprising: a heat exchanger; a tap configured to tap air from at least one of the more upstream locations in the compressor section, pass the tapped air through the heat exchanger and then to the cooling compressor (114; 150), the cooling compressor (114; 150) configured to compress air downstream of the heat exchanger, and to deliver air into the high pressure turbine; a cooling compressor valve movable between two positions, with a first position delivering air from the cooling compressor (114; 150) to a line heading to the high pressure turbine, and in a second position delivering pressurized air from the source to the rotor of the cooling compressor (114; 150); a precooler; and a precooler valve movable between two positions, with a first position allowing air from the precooler to move downstream through a part to an aircraft to which, in use, the gas turbine engine is mounted, and in a second position, blocking flow from the precooler to the aircraft, and allowing pressurized air from the source to pass through a conduit to the cooling compressor valve. a heat exchanger; a tap configured to tap air from at least one of the more upstream locations in the compressor section, pass the tapped air through the heat exchanger and then to the cooling compressor (114; 150), the cooling compressor (114; 150) configured to compress air downstream of the heat exchanger, and to deliver air into the high pressure turbine; a cooling compressor valve movable between two positions, with a first position delivering air from the cooling compressor (114; 150) to a line heading to the high pressure turbine, and in a second position delivering pressurized air from the source to the rotor of the cooling compressor (114; 150); a precooler; and a precooler valve movable between two positions, with a first position allowing air from the precooler to move downstream through a part to an aircraft to which, in use, the gas turbine engine is mounted, and in a second position, blocking flow from the precooler to the aircraft, and allowing pressurized air from the source to pass through a conduit to the cooling compressor valve.