Depends upon what the Dolphin is covered with.

Phoenix use two types of covering. A sticky adhesive backed PVC or what Americans call "shelf-paper", and a proper heat activated adhesive backed 'plastic' covering film like Profilm aka Easycote, Oracover or Ultracote depending upon in which part of the world it's marketed.

I suspect the Dolphin will be covered with the former, as Phoenix in particular up until quite recently covered the majority of their models with this. That's the bad news for your situ as PVC covering is not really heat malleable. If you apply heat, it will simply shrink and shrivel up more, and if you apply too much heat, it will burn through very easily.

If it is Profilm et al, then if it's been heat shrunk beyond its elastic limit, it becomes brittle, separates the colour layer from film and its adhesive becoming difficult nigh impossible to flatten, reform and re-stick. If this is the case, again, the options are repair by patching or recovering with new film. White or Navy Profim is available pretty much at any LHS priced at around $30 per 2m roll.

Sounds like someone executed their own economic triage fixing the problem by selling it to you. The practical solution is simply to cut away the affected area and patch it. The issue such that it is, is purely cosmetic and won't affect performance. Just make sure that oil residue can't seep in. The perfectionist fix is to recover it. I would opt for the former. PVC covered models are a PITA to repair back to original appearance if damaged.

In the interim if you want to fly and until you make up your mind what you want to do re the issue, just use some 3M clear all weather tape to cover/patch/seal it and fly. You can buy it from Bunnings for about $12 per roll. Great stuff. No flight box should be without it.