I recently purchased a cabin that has well water and a hot water heater that is run off the oil furnace. I shut off the well tank when I left but forgot to shut off the hot water heater. Does anyone know if I can damage the heater by having the main water shut off and leaving the water heater on?

Depending on how well the system is sealed, you will start losing water from the water heater fairly quickly.

Without that water being replaced, I would think eventually, you would run dry, but still be heating the empty tank.

Can't be good for it, I guess the bigger question would be, how long before you plan to turn the water back on?

If it's going to be a while, I think the hot water heater should be shut off as well.

Two types of damage can occur and like progunr mentioned, it depends on how tight your system is sealed. If you have a check valve or backflow preventer pressure can build in the heater itself as the hot wayer expands. No back flow valve then you are OK. I don't really picture the tank running dry so I would not worry about that issue. I would worry about a hit water pipe bursting from the increased pressure. I have a cabin and shut all water and fuel use off when I will be gone for more than 2 or 3 days. I can now also control my heating and ac via a telephone linked thermostat, I call the cabin and punch in afew codes and the place is comfortable when we return.