Is your house built on a slab? Do you know if your water lines run under the slab? The more common reason for this is a hot water leak under the slab. A second reason is a defective or worn single-handle faucet that is allowing a cross-over (i.e., mixing hot with the cold) and depending on where that is, could affect nearly the whole house. If the dip tube broke off in the WH, it would be adding cold water at the top (where the typical outlet is) rather than directing it down to the bottom...in that case, the tank without use would be hot, but as soon as you started to use it, the hot at the top would be diluted with the incoming cold. There are probably others....
Do you notice a place on the floor where it seems warm, or if you have pets, have they migrated to laying on one particular area they may not have been using before?