On a basic level, the temperature in any room is defined by the balance of heat input to heat losses.It would take some floor plans of your house to give you a precise answer on this.
I understand both rooms you are talking about are on the same level, but with the bedroom having a regular 8-foot ceiling height, in comparison to the greatroom that has a ceiling height of 16 feet.
Usually the problem with such configurations is that the heat rises in the greatroom and it does not get warm enough. Assuming that you measure the temperatures given a few feet above the floor in both rooms, your greatroom must be substantially overheating as it will be much hotter near the ceiling.
In general I recommend when building structures with such different ceiling heights or when fitting them with a new HVAC system to switch to radiant floor heating.
- Radiant heating can be precisely controlled in different zones.
- And the fact that you are heating the floor rather than the air first slows the effect of the heat rising to the highest rooms.
More accessible options
Adding radiant heat is a large project for most homes, so let's look at your other options.
- Increasing insulation is definitely a step in the right direction,
- but most likely you will need to alter the ductwork if you have a forced-air heat system to have it dispense more heat to the bedroom and less to the greatroom.
You can do this by subtracting an air register in the greatroom and adding one in the bedroom, or by altering duct diameters, as the warm air will always flow the path of least resistance (more air will flow through a large duct, especially if it is short, than through a narrow or long duct).
Properly balanced temps will reduce energy waste
Properly balanced temperatures in the house are essential to lowering your carbon footprint, because the heat loss through a wall or roof is proportional to the temperature differential from the inside to the outside.
If you overheat your greatroom just in order to get the bedrooms acceptably warm, you waste a lot of energy because the temperature differential at the upper wall area and the roof of the greatroom is much larger than it needs to be.
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