Fireplaces - wood burning and vented gas fp's SUCK at heating - literally.. You have to vent, to release the CO. But all the heat goes with it. Conventional fp's can suck the heat out of yr house, making other rooms colder.
You should get a ventless gas unit. These units use filters (charcoal, etc) to remove CO, but recirculate the heat. It's the more efficient, and easier to install bkz you don't have to deal as extensively with your flue. Have an experienced installer put it in, so they'll deal with your flue the right way; though.
The fireplace still has to have a source for combustion air, though. If it uses the house air, then the house has to get replacement air from the cracks around yr windows/doors/attic. This gives drafts, making the house seem even colder. Newer homes are tighter and have to have external air intakes (ducts directly to the outside). Like high efficiency furnaces, this relieves drafts in the rest of the house, but if the installer doesn't seal that external duct properly (darn my big box builder!!!), you'll get drafts around the FP when it's not in use. If your ventless system requires an external air intake (the better ones do), make darn sure that your installer provides a mechanism for shutting and sealing it between uses.
Arguably, since fp's are only used a fraction of the time, more thought and care should be given to how it functions when OFF than when it's actually ON
FYI, if the back of your FP is a solid piece with faux brick grout lines, it's likely an enclosed firebox and can be ultimately removed. If your chimney from the outside is enclosed in siding and not bricked all the way up, it probably was inserted after, and can be removed. If however, it looks like real brick and the outside is bricked, and yr house is older, there's a good chance it's structural, and you can't really remove it economically. You'd have to insert something over it.
My advice: seal up the fp, paint a fake one on the wall, and install radiant floor heating