"How much does it cost to heat a space like this?"
|Great room view looking across dining, kitchen and living room. The house plan can be purchased through Simply Elegant Home Designs at Hudson Simple Cottage House Plan|
Unfortunately there is no good way to answer this question. There are simply too many variables involved; however I can give you one big generality. Warm Air Rises and Cool Air Sinks - In the image above warm air will tend to rise towards the peak of the vaulted space. Therefore, in warm climate regions high ceilings tend to be sought after because you don't want the heat near your body. Conversely, in cold climate regions ceilings tend to be lower where you want to contain as much of the warmth as possible.
Warm Air Rises - Is one of the basic rules you should consider when designing an energy efficient house. To me energy efficiency is the most important aspect to Green Design. For more of my Green Design thoughts you might check out the following:
keep it simple
top 10 green things to do