For electric underfloor heating it does indeed tend to be a sensor in the floor, as the electric underfloor heating is about heating the floor for that nice feel on the feet. For wet underfloor heating I've more commonly see an air temperature thermostat - after all it's probably the main source of heating and the objective is to get the air temperature right. Some do have both air and floor sensors.

The answer here, OP, is to insulate the floor. What you're describing is classic retrofitted UFH, with inadequate insulation. The room gets nice and warm, the heating turns off, and the floor cools down fast. When the floor is insulated, the floor loses its heat to the air, so only if the air is too cool will the floor be too cool, and in that case, the floor will switch back on.