The Search For Barta
You will be able to access this sidequest after talking to Riju to unlock the Thunder Helm, which you can learn about here.
Go to the soldier's training quarters and talk to Liana. She will learn that Barta, the Gerudo who you had to rescue at the Yiga Clan Hideout, has gone missing again. Barta apparently wanted to go investigate "leviathan bones" and left of her own accord. Unfortunately, where she went is so hot that even heat-resistant gear can't protect you from damages. And the Gerudo don't seem to be exempt from it either, so let's go find Barta and bring her back.
First off, grab a Hearty Durian before you leave. This will save you the trouble of having to go back and forth. If you don't have a Hearty Durian, you can actually buy one from the Gerudo Town general store instead of having to go gathering (but of course you can gather if you want).
If you have already discovered the Great Fairy Fountain in the far southewest corner of Gerudo Desert and the Hawa Koth Shrine that's near it, you can simply fast travel there. If not, ride on a sand seal in a straight southwest trajectory. You will go through a sandstorm but do not deviate from your path.
Eventually you will arrive at the Shrine and the Great Fairy Fountain standing amidst the giant bones of some long-dead creature. Barta is right behind the Shrine, underneath the tip of the snout of the skull. Talk to her and she will want a Hearty Durian. Give her your Hearty Durian and she will leave back to Gerudo Town.
Speak with Liana back at the soldier's training quarters and for your troubles, you will be given a silver Rupee worth 100 Rupees.