One of the reasons you had such high heat was probably due to the lack of ceiling insulation.
Another reason is heat migrating off the walls.
The first things you need to do in that space are to insulate, insulate, insulate walls and floor to R21 and R38. Once you do this and provide sufficient venting, problem solved, although vapor barriers would have helped, it is cost prohibitive to rip down walls to put in the plastic.
I don’t define the area above as the heel. The heel is the amount of space between the bottom of the roof boards and the top of the walls. This is where soffit vents go… In newer homes “energy” heels are required, something like 7″ or so, I forget the actual spec. You probably have 3″ heels or so..maybe less…hard to say from here.
If you have another roof intersection in the middle, your old house roof should have openings for that new house addition, unless space doesn’t permit. That new house addition can be equipped with ridge vent based upon your limited description, combined with gable vents and/or mushrooms and soffit venting, this would be an effective venting solution.
Additionally, if the heels (my definition) are closed up with blocking, remove it and vent all the soffit you can.
If you install a ridge vent on the new roof, don’t install a gable vent on the end of it, those are useless when combined with ridge vent. On the other hand, adding gable vents to the original house would be a good solution because you have no exhaust venting in that section except for in the middle given you cutout to a ridgevent.