How can I evenly heat a house with a partial basement, as shown in the diagram below? The rooms over the slab are consistently several degrees cooler than the rooms over the basement, particularly when the doors are closed for a while.
The portion of the house on the slab foundation is heated from ceiling vents whereas the portion of the house that is over the basement is heated from floor vents. The ceilings are 9 feet high, which may contribute to the inability of the heat from the ceiling vents to circulate throughout the rooms.
This is a new house with good insulation and windows. The portion of the house over the basement is mostly one open space, whereas the portion of the house on the slab is divided into two bedrooms and two bathrooms.
I have tried closing or mostly closing the vents in the portion of the house over the basement in an attempt to get more heat to the portion of the house over the slab. Leaving doors open helps the issue some, but it is not desirable to have to leave the doors open all the time.
Is the HVAC for this house set up appropriately? What measures would help heat the house evenly?