What would happen if I plugged a grounded submersible metal aquarium heater into an ungrounded outlet?
Shut the power off to the outlet and remove the plate. There should be a ground in the outlet box. Wire nut a similar piece of copper to the ground (uninsulated) wire and make it long enough to make it past the thermostat to the grounded prong on your plug. Wrap the new wire carefully and tightly around the grounded prong so as to stay completely away from the flat blades, plug it back into the thermostat and Voila! Sometimes the grounded prong has a slit on the underside you can push your wire into. This is OBVIOUSLY a bit McGiverish, but it should work and be safe as long as your ground wire is away from any hot ones. Be Careful!
Just changing the outlet to a 3-prong won’t make it grounded. Start by shutting of the power at the fuse/circuit breaker. Remove the outlet. How many wires are there? In your case, I would guess that there are only two colors. White and black. If there is no bare copper wire, then you don’t have a ground available. An acceptable to code way around this is to install a GFCI. While not technically a grounded outlet, the GFCI measures any inbalances between the hot and the neutral wire. Thus, is you short between them, your trip the GFCI. The problem with this solution is that the hot is still hot. You could also install a GFCI breaker in your panel. That way if it trips, the hot is no longer hot. Be careful though if your fridge is on the same circuit. If it trips, you could lose all of your food in there. It may be possible to run a 14-2 romex from the outlet to your panel without too much difficulty but I’d recommend a license electrician do that for you. They are insured against makin