I doubt this is sun burn. I had some do that to me also with the cold snap. I live in central Texas and we had a drastic temp change in one day with massive amounts of rain. Your plumeria needs to come inside now for the winter and if the soil is really soggy it should be taken out of the pot. I have brought in all of mine. It will continue to drop it's leaves if it has not already. We got more rain coming so if you have not brought it in yet you need to do that now. And for what it's worth mine all stay in full all day sun on my hot deck through the summer. They will not burn from sun if well watered.
