The inside diameter of the chimney used to vent your furnace, should have anything to do with heat loss. If your furnace is 10-15 years old (or older!), it needs to be replaced to make it more efficient.
The idea of getting a new furnace that can be vented out the side of your house, instead of up the chimney, is a good one. However, if your water heater is gas, it may also use the same chimney for venting, so you wouldn't be able to close the chimney up permanently.
If you have an older, inefficient furnace, you are probably already overspending enough on your gas bill to pay for a new furnace that's more efficient (and will put more heat into your living area).