How to keep an attic over the garage cool?
You're basically asking how to convert an unconditioned space into a conditioned space.

This requires opening up the space to the existing conditioned part of the house and closing it off to the unconditioned space.

I challenge your belief that it isn't vented.  I suspect that it is vented - there will (or should) be some kind of air gap between the top corner of your office wall and the roof line.  This is mandatory, as unconditioned spaces must properly vent to the outside to allow airflow which prevents moisture buildup, thus preventing rot, mold, etc.

I won't design the solution for you (plan my project questions for me are frowned on), but if it were me, I would bump the wall out a couple of feet and build a complete closet, WELL insulated, with vents on the top and bottom, with a low power continuous fan running to make sure the air got transferred.