Damage from a frost will not travel down the plant, but rot will. After a frost, plumeria stems that are damaged will turn black, all of the blackness must be cut off and some extra to prevent rot infections that will travel through the plant.
NOTE: Plumeria sap is toxic, especially to your eyes. When trimming plumeria, always wear protective eyeglasses and gloves. Also consider covering your legs and arms.
A frost can come up from the bottom of the plant too. Cut back to the trunk if this is happened and don’t worry. As long as the roots aren’t dead, the plumeria will bounce back.
After frost cut dead stems immediately. Take a cut to where you believe the black and gunk end. Then take one more cut to be sure. It is imperative that after each cut you wipe your cutting blade clean with rubbing alcohol or peroxide. It’s very easy to spread bacteria and fungi that can effect the plant.
Seal the ends with a pruning sealant like lime paste or DAP.
Monitor if the plumeria, if black rot continues to spread, quickly cut and seal. Just cut all the rot off the plant.
Water the plant enough, but don’t drowned it. The cold damage is worse on a weaker plant.
If the plumeria is in a container, move the plant closer to the house or a wall where the sunlight has warmed it all day (radiating heat). If the plant can’t be moved, cover with frost cloth.
Do nothing. If some of the dead leaves on plants are unsightly you can cut them but they may also act as a protector for the new tip growth on most plants.