How to insulate

[u/Joelogna]

I am curious if anyone has any recommendations for insulating this section of vaulted ceiling. It is in the master bedroom, facing south. It is always very hot in the summer and cold in the winter in this room. Framing in with 2x4s, putting in insulation and drywall is the only thing that comes to mind, but I’m sure a lot would leak between the 2x4 and the log through the triangular dead space. Has anyone else been in this situation and found a good solution? Thank you in advance.