A cheap way out of this, is to light an incense stick in the room in question. Then whatever direction the smoke is blowing, your infiltration is coming in behind it. Then concentrate your IR scan in that area. The slightest of cold air infiltration is not that hard to locate with my B-2.
When I earlier looked at this pic, I thought that the floor had no insulation as the ceiling drywall was warmer than the bottom of the floor joists. If there is no insulation, the heat will also radiate downward and the ceiling becomes a heater (well, partial heater} for the garage below. If the radiant floor system was designed correctly, or even a bit oversized, for the room above, it will not heat the room on the worst days as a signifcant portion of the heat is moving downward by radiation. With a fully open floor cavity, air infiltration/exfiltration may have no resistance at all if the air barrier system was not the main concern of the GC.
The solution would be to blow the floor cavities with insulation. My usual choice is blown cellulose (due to its recycled content and it does a better job of restricting air infiltration than other loose blown insulations). In this case, with the floor joists on 24" centers, not 16", and not knowing the joist depth (hence total weight of materials that would be installed), I would use a lighter weight blown fiberglass so as not to have too much weight on the drywall and potentially cause other problems later.
You need to be looking at the HVAC system more and not necessarily the building envelope.
Insulation does not “make heat”.
It can not keep the heat in, that is not there.
Concerning the insulation capacity of the flooring system, this can be done with calculations obtained through infrared scans. This is taught at the building science course at ITC.
The room over the garage (here we call at the bonus room) has the highest heating and cooling load of all the rooms in the house simplyalmost all of the square footage of the ceilings, walls and floor or against a non-conditioned space. This room, because of its location is often difficult to get sufficient air flow to. Insufficient air equals insufficient BTUs.
These rooms are often large with cathedral ceilings containing large volumes of air. They often do not have a return air duct which is necessary to condition large volume rooms. If you don’t take the air out to be conditioned you substantially reduce the capacity to heat the room. Trying to mix hot and cold air is also inefficient due to air stratification in the properties of air. Hot and cold air mix about as well as water and oil. Adequate mixing of the year requires sufficient the lost city which is the bonus room frequently cannot produce.