If you just have a small electric strip heater that is too small for the sunroom, it would hardly ever shut off in the very cold weather and cost a bundle. I just bid a job with a similar problem for a large sunroom for 2400 for a 60000btu wall furnace. I would suggest a propane wall furnace be put in. Williams brand wall furnaces are dependable. Smaller units up to 30000btu are just a couple feet high, and larger units are around five feet tall go up to around 60000btu. You can vent them through the wall or roof depending upon the model you choose. They operate just like a regular furnace by thermostat, and they have a filter. They are only in the 80 percent efficency range but with electric rates on the rise, propane would be the better choice over electric. Another option would be to add a zone off the ductwork of your current furnace that would modulate a damper and cycle the furnace when there was a call for heat. Being that you only keep the setpoint at 55 degrees you should be ok. However the energy useage would be about the same, and the installation and equipment costs would be higher than the wall furnace.

Other heat sources will fare no better unless they have no monthly cost after installation, like solar. Best bet is to insulate. This is also much much (did I say MUCH?) more cost effective.

I would go with a wall furnace or if you'll be using the room a lot possibly a pellet stove.

you could insulate till your blue in the face, I would imagine a sun room has many windows. Also the propane heat would use more propane (not a whole lot at a 55 degree room setpoint), but it was the high electric bill that was the complaint.

Insulate the windows as well. Cheap, cheap, cheap.

What do you mean "Insulate the windows as well" ?

I think he means cover them up with foil-faced insulation board.

More likely this is what he meant.

HTH
Chris

Here is a link that might be useful:

Hey, now there's a good idea. Another option is to install magnetic windows to cover existing windows. They go on the inside, not the outside. They attach like a refrigerator door seal. They create a dead air space at each window, they stop the air infiltration around the frame, and they block UV rays, so fabrics don't fade, and radiant heat from sunlight is reduced. There are companies that do this for you. I have not priced them in a long time, so I can only hazard a guess at cost; maybe $100-$200 per window. Maybe less, maybe more. If more, not much more.
To insulate the floor, check out a product called reflectix. I think they have a .com. Excellent R-value!
These are the most expensive suggestions I have. There are cheaper alternatives, and I am sure you will have no problem finding them on the internet. The nice thing about them is after they are installed they consume no energy, so there is no monthly bill.
If you want to go this route, DO NOT hire a hvac co until the job is done. Don't even talk to one. After the job is done, if you still need heat, have at least three hvac co's do a load calculation on the room, so they can accurately determine your best options. If a hvac co says it doesn't do load calcs, don't bother with them, because they will tell you whatever you want to hear.
By the way, I work for one of the top 10 rated (by Georgia Power) hvac companies in the Atlanta metro area, and I have been in the business for 12 years.

Of course, radiant heat from inside is increased.