I tried something similar to this once, with a desk-drawer computer. Worked ok, I think.
First thing I would do is cut two holes in the back of the desk; one to match up with the PSU, and one to match up with the intake fan (assuming you have one on the back). Then get two pieces of PVC tubing that will allow you to close up as much as possible the computer and desk holes, so you're blowing as much warm air out as possible, and sucking in as much cool air.
As the other guy said, USB is limited to 5V, and < 1A, I think (maybe even 0.5A). That's not going to drive much of a fan. Can you just remove most/all of the back area of the enclosure? Especially the top section? That may give you enough ventilation as-is, without any fans to assist. Again, I'm make sure in particular that the fans pushing hot air out of your case can blow directly out...
Clint