Rehabbing to Rent - Need Ceiling Insulation Thoughts

So I'm doing major rehab of a 5 unit in San Diego and scratching my head on one particular "feature" of the buildings. The ceilings are really nice vaulted open beam ceilings with stained ship lap tongue and groove finish between the bay's - it's visually the nicest part of the units. Turns out the roof is - literally - 1x6 tongue and groove, then 1/2" sheathing, then roofing paper, then shingles. No insulation at all. This is San Diego and maybe 4 miles from the ocean, so it's a temperate climate. But, man is it going to be warm in the summer and cool in the winter. There's no A/C. Would you insulate the ceiling in this situation?