As a drake you gain incredible speed, so as long as you have a way to deal with the damage you should be okay.
Do you have any source of regeneration? Having Immune to Pain helps a lot as well, as does a high First Aid skill. If you are lacking in such tools, you might need to rely on healing with prayers and the water orb.
As for items burning, you can wear higher metal items without any problem and iron items will usually survive as well, especially if they are blessed and if you have maximum luck. Make sure you are at good piety and wear the Ankh.
Remember that huge stacks of items will survive in the tower with minimal damage as well. Like if you have a stack of 100 spenseweed, you won't lose too many of them.
Not sure I really need to say this, but leave valuable stuff like SoCR at home.
Now the big problem is that your digging tools burn. It is best to do a scouting run first, where you find out where the stairs are and how to get to the top the quickest. Afterwards you do the real run, where you bring as many digging tools as you can and run to the temple. Maybe even sacrifice your wand of teleportation to get there faster, if the stairs are far apart. Once you breached the temple walls, the rest is straightforward.
If you lack digging tools, a good place to find more of them is Darkforge. Once you have killed most of the steel golems, dwarven chaos knights will start to spawn. Those often drop a pickaxe or a wand of digging.
You steal a scroll labelled HITME. The orc hits you.