My first attempt to resolve the problem failed. At least I can narrow down the possible culprits now, hopefully. Unless it's not simply caused by completed quests...
I know the save I started from is okay. So, to keep track of the possible culprits, these are the quests I completed before entering the desert:
- Holy Smite
- Needs More Iron
- That's Cold
- Evil Puppy Cull
- Leave No Witnesses…
I din't count She's As Cold As Ice and Slush Puppy Love (And Hate), because they're necessary to reach the dessert, so they can't be causing the problem.