It would in fact fall to the same temperature, given enough time. Unless the laws of physics are broken, the temperatures will eventually equalize.
However at some point, depending on the level of insulation, the amount of BTU you lose per hour is so small as to be eaten by local temperature differences outside, and by then the temperature outside starts increasing again.
Additionally, there are other weird impacts you have to take into account that don't normally matter. For example, your water/chairs/tables/etc have some heat capacity, and when the ambient air around them gets to a high enough temperature difference, the BTU they transfer into the air will matter (particularly because water holds 62 btu per lb (or something like that) and air only 0.02, so 1 pound of water can heat a lot of air :P. Wood is similar )