When you arrive at the Bazar outside the Gerudo city, you will be unable to go any further as the desert heat will cause Link to lose health. In order to get to the Gerudo city, you will need something that will allow you to withstand it. How do you make it through the desert heat without losing health?
There are 2 methods to achieve this. Due to the primary quest that is involved, you will end up needing both methods. The first is to cook some food that will keep Link cool. If you look at the store, there are a stack of watermelons. Buy one of these and cook it to get a meal that will grant you some resistance against the heat. One will be enough for you to make it to the Gerudo city, provided you don't stop to chat or fight any enemies. Once you get to the city, you can begin the quest line for gaining access to the Gerudo city.
The second method is using an armor set. There are a few sets that can provide this resistance, but the one you will find in this region is the Gerudo Vai armor set. In other words, female Gerudo clothes. You will get this as part of the Forbidden fortress quest line, so I won't post any spoilers here, but if you need to know how to get it, check out the guide on obtaining the Gerudo Vai armor set in the walkthrough.