this is what I thought was going on here. your pictures just confirmed it.
now you understand the link I posted in relation to your situation?
so you actually have two situations of bump outs.
one at fireplace & one at cabinets (??)
that neither of the bumpout walls are insulated, contributes to the temp diffrences.
so you have choices as to how to deal with them.
easiest would be just to foam from basement where cantilvered joists exit
walls. this would stop air movement, but still leaves a big uninsulated area of wall.
harder would be to open the bump outs..fireplace from under deck at floor of bump out..
then foam the walls, fit foam sheating to bottom of bump out, air seal and replace osb sheathing.
then from inside basement do the final air sealing.
the other bump out..no access from underneath? then take off vinyl open wall
foam, foam sheath opening & air seal then replace osb, re-install vinyl.
just as you seal joists thru bottom of wall..you have to check at top of the
bump outs for the same situation.
foam insulation would be faster & easier, but I beams at openings make it
easier to seal than space joists. if you use foam sheathing you fit it tight
& caulk it in place. so, I disagree with your energy rater on that one.
and not now..but later explain the radiant barrier in pic five.