I would hate to drill holes in an antique; but, you do need to establish PROPER ventilation and the key to that is an adequate entry for cool air along with a controlled exit for warm air.
Since the system already has fans blowing warm air out of the box, I would take some corrugated cardboard, create a tunnel that fit against the towers exhaust fan(s), get it lined up properly, drill several holes in the trunk (or cut one big one), fasten the cardboard guide to the trunk, and then place the tower so it rests against the guide.
The pretty way to address the intake would be to raise the trunk off the floor (about an inch) and drill several holes through the bottom of the trunk near where the front of the tower will sit.
As notes; when I say several, I mean 10+ square inches of holes (hundreds of 1/4 inch holes, fewer 1/2 inch holes) and the goal is to have an adequate and controlled intake and exhaust. Most towers have exhaust fans in the power supply and maybe just below it (Dell's do). Most towers also take in air at the bottom of the front faceplate.
