Any Solar Guru's out there?

We heat our house with fireplaces....only one problem is that the bathrooms don't have any.
So, in the past we have used electric plug in heaters, but coming up on the cold season our CFE bill will spin out of control.
There is nothing more than I hate to see the electric meter spinning around like a hamster in an cage, when we use the electric heater (s).
We use Solar to preheat our water, and that is pretty efficient unless we don't have any sun for 3 or 4 days during the rainy season.

What I was thinking of is why couldn't I lash up a basic hot water, radiator type heater just for the bathroom?
My plan was to buy some 3/4 or 1 inch black PVC pipe, fan it out in a large concentric circle, place it on the roof, along with a small solar panel and pipe it into the bathroom.
Under our solo window which faces the east, I would install a radiator kind of heat exchanger, maybe one of those hot water radiant baseboard heaters, and see what happens.
The solar electric panel would power a very small pump that would circulate the hot water through the system and would only work during sunlight hours, so that would be the basic limiting device, so that it wouldn't run during the evening when there was no sun.

Reading up on some articles the only hassle I see is that the pressure of the hot water inside the PVC may exceed the pressure and temperature limits for the hot water.
We can't put a copper unit up on the roof since , that will turn up as someone's sink or art object within a short amount of time.

Can't think of any other cheap way of heating that one room, the total square footage is about 150 sq feet or less.
I would put a wood stove in there, but there is no convenient place to position it anywhere in the room that would make any sense.

So, back to the research to find the cheap and dirty way to heat that room.....Any suggestions would be greatly appreciated......