The fire damage is quite minimal, and I've not noticed it breaks hide. The bigger problem is whether any of the mobs inside the pyramid see invis. If they do, get ready to be hit by up to 20 or so HT's at once.
I've not been to Fear since getting the Shroud of Stealth AA, so I haven't had a chance to see how well that works, if at all. I hear that Fear mobs are notorious for seeing through SoS.
Get a runspeed buff like SoE, run into fear, run around and pick up a big train. Run your train to the ring of fire, and circle the temple, pulling your train over/through the temple. This will add every mob in the temple to your train. Run back out of the fire ring heading south (stay way from Cazic if he's up), run in a big circle making sure you stay well ahead of your enormous train. Head back through the fire wall from the southeast, run up the ramp on the east side to the second tier of the now-empty pyramid, run around back to the opening, run in, take all lefts and zone. This only works if you stay far enough ahead of the Amys to avoid getting HT'd.