Even if insulated, a bedroom over a garage will of course be colder in winter and warmer in summer because one of its surrounding sides is colder/wamer, respectively. Heat and cold "travels" vertically more than horizontally. There also is no better insulation than the Earth: losing that advantage underneath understandably changes the equation for that room.
You can and should boost the insulation. Check through a test hole if it is there. If there is no insulation, the easiest, least intrusive way would be to blow it in through holes in the garage ceiling, although that can get be messy because you are blowing it up, not down, near the input holes and gravity will work against you.
You can also tear down the drywall, install rolled insulation "upside down" between the beams (with the paper vapor barrier on the top "toe-stapled" to the top of the beams so that it is on the warm-in-winter side), and re-drywall if you feel ambitious. You can use rolls without an attached paper vapor barrier, also. But if you do use the more common rolls with an attached vapor barrier, make sure you do not install it with the paper vapor barrier facing down, even though that will seem the "logical" and "tidier" way to install it. Otherwise, moisture will condense inside the insulation during winter due to the change in dewpoints and humidity between the cold garage air and the warmer, humid interior air. The condensed moisture will mold and rot the insulation.
If you do find insulation, try gently sawing out a piece, pull it down, and look up to see how deep it is. If it does not fill the cavity between the beams, or if it looks old and compressed, you can insulate with higher R-rated insulation.
Second, over-garage rooms are also usually more remote from the air blower in a central air system and sometimes receive lessair from the blower, not more air that they would need given the colder/wamer floor and lesser insulation. Close some vents elsewhere so as to force more air-conditioned/heated air to that room. Close the vent in the room with the thermostat, because that controls how long the blower blows. I can't imagine that not having some effect. If, as you said, that does not work, you might want to see if you can use wider ducts to service that room, or insulate the ducts to prevent temperature loss in transit.
You also might want to consider installing a thermostat in that room or using a dual-thermostat system that shuts the ducts to other rooms and opens only the ducts connected to that room if the thermostats indicate that only that one room needs more air conditioning/heat. It is more expensive, but it might be worth the expense if it is such a problem that closing other vents does not work.
[This message has been edited by Lawrence (edited September 13, 2002).]