Thermal Mass Puzzle I Can't Figure Out
Thermal mass does not block heat; it stores and releases heat, and it slows down the flow of heat. It will absorb heat when it is colder than the surrounding area, and it will release heat when it is warmer than the surrounding area. These characteristics are useful in the following circumstances:


A thermal mass wall in a climate/season where the outdoor temperatures cycle above and below the indoor comfort point. The heavy walls will slow down the flow of heat so much that by the time it reaches the interior, the outside temperature will have dropped, reversing the flow of heat out of the wall. In order for this to work, the wall must be very dense and very thick; 12" thick rammed earth or adobe, for example.
A thermal mass element within a building's insulated envelope. Such a thing can be used to store free heat generated from sunlight, cooling, electricity usage, etc and store them until the sun goes down and everybody is asleep, whereupon it will release it, moderating the interior temperature and reducing its daily fluctuations, especially at night.


Insulating the underside of the floor is a great idea, as it will make your thermal mass floor fall into category 2.

Preventing the sun from hitting your walls or windows is likewise always a good idea; heat gain is driven almost entirely by direct solar gain.

Keeping the garage door closed may or may not help; try it and see.