My first thought is that wrapping a wood tub with rigid foam will cause moisture to become trapped between the wood and foam thus causing the wood to rapidly deteriorate.
So, I'd be inclined to space that insulation away from the tub about 1/2" so there was a continuous air space between tub and insulation. However, if air is allowed to move, you lose insulative value, negating the reason the insulation is installed. However, a tub insulated in this manner would surely still be better than no additional insulation at all. I just wonder if the benefits would be worth the time, effort, and expense.
Anyone done this or have thoughts?
(by the way, the insulation would be covered by a cedar enclosure for protection and esthetics)