It changes the perceived room temperature even less than actual temperature! As you say, air has little mass and very little thermal mass, solids have a lot mo

It changes the perceived room temperature even less than actual temperature! As you say, air has little mass and very little thermal mass, solids have a lot more thermal mass so the equalized temperature after briefly exchanging all the air for cold air is basically the same as the original. But physiologically and psychologically, human comfort levels are based not on the air temperature and convection or conduction with the air but on the mean radiant temperature, the temperature of an ideal enclosure of uniform emissivity and temperature that creates the same radiant heat transfer rates as whatever non-uniform surfaces are in the area. Sit with your face in a sunbeam in a cold house, and you'll feel like it's pleasantly warm even if the heating of the sunbeam is doing less than the motion of cold air wicking away heat. Open your garage door on a still winter day, standing in the warm air with one wall removed, exposing you to sub-freezing temperatures, and you'll feel cold even if the air is still warm. Stand in the high-temp air blast of a torpedo heater in a cold shop, with the ceiling, concrete floor, walls, and other equipment still frigid, and you'll feel cold even as the hot air melts the plastic bits on your clothes. Blast the AC in a hot car, and you might be breathing air at 40F/5C from the vents, but you'll still feel hot until the vehicle interior trim is cooled by the air.