I am not certain as I'm more familar with the s80, HOWEVER on the S80 the compartment is supplied with air from the passenger compartment by means of a black hose/tube. The end which connects to the box has a fan in it. Cool air from the cabin is drawn in by that fan which works in conjunction with an outlet design which varies.
Originally, there was a draft tube which exited under the compressor area and which was removed when it was realized that it caught on curbs when nosing in and could rotate into the accessory belt and shred it. Then they shortened the draft tube projection. At some point, they also seem to have connected the exit tube to the big fan housing, on the suction side (your original design). The S80(2002) has a stealth tube exit, which removes the pipe from the top front and uses an enlarged cable housing at the bottom for a safe exit. I suspect that the air is exiting somewhere from the housing on your car.