I think that the "hot seat" issue is significant -- the water heater is under the seat --but fortunately, that is the seat where DW sits, and she is the one who wants it warmer! Seriously, if I do this, I would have to monitor the temp to make sure there is no fire danger. I would experiment and then undo the modification if the results are unsafe.
And yes, this will result in less insulation for the tank, when (and only when) I have removed the styrofoam flap. It will mean that we will burn more propane -- but I have two tanks, and we currently use a quarter gallon of propane a day. (I have measured it.)
My real question, though, is whether some of the styrofoam can even be removed at all?? Is it glued onto the tank? I would guess it is not, since there are these nylon straps that go around the tank to hold the foam on. If it were glued, the straps would be useless.
If and when I do this mod, I would probably just use a box cutter to slice the foam flap, and I would probably put velcro on the outside of the flap to re-install it in warmer weather.
Finally, I don't plan on adding a fan to distribute the heat -- I might cut a vent hole in the cabinet to let the heat out. There is a plywood hatch cover over the water heater -- an access panel -- and I could easily cut some holes in that, too.
