There are very few games that have such tedious and frustrating sections where I feel it's simply not worth the aggravation to complete. This is one such section.
As far as I can tell, there's no skill or strategy involved; it's just a massive pain in the ass.
I won't take The Red Prince in my next playthrough.
It's actually not that bad with the right skill setup. The first few rooms are empty, so you can use a combination of two skills to clear the Necrofire from them without incident.
Polymorph 1 + Aero 1 = Vaporize - This converts the permanent Necrofire surfaces to permanent clouds.
Aero 2 = Pressure Spike - This converts the permanent clouds into temporary, 2-turn Necrofire surfaces. You can afford to wait these out outside of combat, and you can get fairly close to some snemies to cast them without getting spotted.
In combat, you have two choices: Bless + something to kill a normal fire surface,
or Tornado (Aero 3). Aero 3 is a tougher requirement, but with Aero 2 for Teleport and a piece of +1 Aero gear you can cast it. There's also a unique staff you can find without combat in
the secret Magister vault
which has Tornado on it. I put that on my 2H Warrior for 1 AP to clear out a pesky surface.
Between my Aero/Hydro mage, my Aero Scoundrel with a +1 Aero amulet, and my Warrior with a +Tornado staff, I was able to clear the surfaces with little problems.