External insulation under shingled roof

We have a 60s-style A-frame with no insulation beyond what's provided by the 3x6 pine planks of the sloping roof/walls. It's oriented east-west, and I suspect the south slope (with a pitch of about 60 degrees) actually helps heat the place in the winter time. But in the summer, the heat radiated by that slope is so intense you can't sit within three feet of it, and the whole place is uncomfortably warm.
Of course, I don't want to insulate over the inside of that fabulous stained and varnished planking. Is there any rigid insulation with a worthwhile R factor that could be placed on the outside of the planks, that wouldn't have to be sheathed over to carry a new suit of shingles?
Or, if the answer is no, what the best material to insulate with, assuming you're willing to sheath over it?
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Hi.
We also have a 60's style aframe, we are in Sonoma County california. We had some fire damage and are looking at what insulation to put in for the remodel. We've been looking at rigid and cellulose insulation, rigid seems to be recommended. Any thoughts? Its 24 feet to the peek of the a-frame, and we heat with a wood stove.
Thanks,John
LFM wrote:

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