If this is just a grass fire, I suppose you could take a deep breath and run through the flames into the already-burned area.

Where trees and underbrush are burning, which could probably be thought of as a mini-firestorm, you aren't just dealing with the radiant heat from the fire, but the high ambient temperature. A true firestorm can create temps of 2000F (yes, that's two thousand degrees).

The few people I have heard of that survived conditions like these were a few people in Australia who had underground shelters just for that purpose. Their shelters were pretty highly insulated (thickly covered with soil), and had a stone, concrete or mud brick dogleg in front of the door to shield it from the radiant heat that would have set the wooden door on fire. (I suspect that a metal door, while more fireproof, would also transfer heat into the shelter.) It has been recommended that if you might have to depend on a shelter like this, to build it in an open area, and keep the grass around it very short.

But realistically, depending on what you are carrying with you, in a good hot fire, you're probably going to die without a serious high-mass shelter around you.

Given 24 hours, you'd best pack your gear and head out of the area.