Walking repeatedly in 'shade' spaces will eventually cause your exposure to lower and give you more time to wander the desert! Keep an eye on the UI and sound effects to know when you get more stamina.
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I managed to make it to the cabin but I really feel it's either not clear enough or too harsh in its present state.
Considering I made it to the cabin by the skin of my teeth I'm certainly not eager to continue on into the desert, especially with an apparent lack of auto-skip for defeat scenes meaning I gotta mash the spacebar to be rid of the mirage defeat scene.