An auxiliary power unit for an aircraft, having a compressor, an intercooler including first conduit(s) having an inlet in fluid communication with the compressor outlet and second conduit(s) configured for circulation of a coolant therethrough, an engine core having an inlet in fluid communication with an outlet of the first conduit(s), and a bleed conduit in fluid communication with the outlet of the first conduit(s) through a bleed air valve. The auxiliary power unit may include a generator in driving engagement with the shaft of the engine core to provide electrical power for the aircraft. A method of providing compressed air and electrical power to an aircraft is also discussed.