You might think of adding some heat. There are some new idea's in heating See this companys website Mitsubishi Electric and Electronics USA

Have you looked into electric baseboard heaters? It may be the way to go.

You can also try Energy efficient space heaters that can be purchased from most domestic appliance retailers.

Good retailers will be pleased to advise prospective purchasers about the energy efficiency of a device and provide information about effective usage. Eco friendly stores may also be able to offer advice on local alternatives.

If it's a full conversion and well insulated, just cranking a space heater in the room for a bit will keep it warm for a while.

You've had good experience with them, Hudson? Are they really 4x as efficient as traditional designs?

Make sure it was insulated before it was converted. Baseboard heaters are nice. I assume there is a vent from the central heater. Maybe close some vents in other rooms so more comes out in the family room.

A pellet stove is a good source for a room like this, they can be direct vented through a wall. The fuel that they use is often waste wood, or made from already dead trees (we have pine beetle problem here in the west and a few pellet manufactures have set up shop)

A pellet stove can put out a bunch of heat and even be put on a thermostat to operate automatically. ...»

I work for a lady in Helen who had them. They worked very well and with the placement over her sliders it kept the cold from wiking though the glass. I really liked them and the fact that they blow down the air from above was nice. Now I did not see her power bill but they seem to cycle as a normal unit and did not run 24/7. Oh and they are 220 set ups so the power usage was much less than a 110 window unit.

Sounds excellent! I really enjoyed reading about them : )