HC (and hovering) you're right that friction (and contact with hot surfaces) raises the temperature, and these are the main mechanisms by which gearbox oil (an essentially incompressible fluid) heats up. These processes undoubtedly have a role to play in the compression heater or 'Roots Blower', but they are not the main one which is compression.
P1*V1/T1 = P2*V2/T2 is the combination of Boyle's and Charles' Law which guides you here. If the pressure and volume were the same on either side of the roots blower, then there would be no temperature rise. It's only where the compressed air is maintained at a higher pressure that the air is 'charged' ie. hotter.