True, compressing any gas (air) generates heat and allowing it to expand absorbs heat (that's the "refrigeration cycle" in a nutshell). However, the friction of the gasket sliding along the pump tube also warms up the walls of the pump. If the pump were "frictionless" it wouldn't heat up so much. If all the heat came from merely compressing the air, the tire, pump hose and pump cylinder would all heat up more or less equally. They don't.