Is there a name for this type of ceiling? It's angled, so the roof is directly above the room (no attic). There's also a higher wall whose top portion is presumably adjacent to the attic.
I've seen this in California homes, including my own master bedroom. It really heats up during the day, presumably due to heat convection from the roof and attic.
Typically there isn't a lot of room between the ceiling and the outside roof and the insulation they use in that space doesn't provide enough protection from the heat and cold. This is an area that is ideal for Spray Foam which provides superior insulating properties.
The problem is less conditioning the extra space and more the fact that a good R-60 roof requires about twenty inches of fluffy insulation between the drywall ceiling and the roof deck.
I've seen this in California homes, including my own master bedroom. It really heats up during the day, presumably due to heat convection from the roof and attic.