Why is the room over my garage cold?

Short answer: Because the garage is outside the house's insulation, and air moving through the floor framing pulls the heat out. The DOE says the floor over a garage must be insulated and air sealed just like any exterior walls or floors above unconditioned space [1].

What is going on

An attached garage is still outside the thermal envelope [1]. If the floor cavities over it are not sealed, cold air moves through them. The DOE: The moving air pulls heat from the floor system, robbing the insulation of its effectiveness and causing cold floors above [1]. Air sealing also keeps car exhaust and chemical fumes from the garage out of the house [1].

The knee walls

Bonus rooms usually have short knee walls with attic space behind them. The DOE says these can leak a lot of air if there is no continuous air barrier, and calls for blocking in the joist bays under the knee walls to stop air flowing under the room [2]. ENERGY STAR says the same: You need to plug these cavities in order to stop air from traveling under the floor of the finished space [3].

How we fix it

Seal and fill the floor over the garage, with batts or foam depending on access, and deal with the knee walls and the open joist bays under them. Closed cell foam does both jobs at once on a floor; the DOE notes it can serve as the air barrier at 1.5 inches or more [1].

More questions

Can spray foam fix a cold floor over a garage?

Yes. Closed cell foam in the floor cavity can serve as the air barrier at 1.5 inches or more, per the DOE, and insulates at the same time.