Density of heated water is less than cold water so it wants to be on top. So yes, hot water does expand ever so slightly until it becomes steam and then you do notice the expansion! Water also expands when it goes solid, less dense so it floats. Most liquid to solid changes get denser, so water is a odd duck!
You need a heat sink, aka heat dump, that can dispose of the extra heat. A large 1000 gallon water tank would do, a Modine or extra baseboard radiator.