Wow- this thread is really warming up! Thanks for all the comments so far, y'all. I'm thinking I will be starting with a space heater- that buys me some time to figure it out... I like the thought of a diesel heater, I think.
As for the 'plug' on the hot water tank, that will be the first thing I'll check! Cause that would solve all the problems- at a far lower cost.
On the space heater: oil? Ceramic? Infrared? Does it really matter?