The heat is not the enemy, the lack of high temp anti-seize is the enemy. I soak them in PB Blaster...and sometimes they will let go, but more often than not, I end up right where you are. Cast is one of the finest products to rust up in a very short time, hence you MUST outsmart the process. For all those who haven't been there yet, DO NOT try it right now, but it won't hurt to soak the screws right now and see if next week they will loosen up. If not, grind them flush, get a high quality center punch, and drill it out. Perhaps it will let go for an ezy-out, but no guarantees. If you see a Snap=on truck, you can flag him down. I like Matco and Mac myself, and Sears has lots of products for this purpose.
PS: WD 40 won't loosen the rust, but your favorite penetrant will work over time. If none of these things work, you can call the manufacturer and order a new door( or if you have a short fuse and smash the damned thing.....)
I know someone will talk about the left hand drills that are so popular. Great idea, and if they work for you, congrats!