I've already beat the other three divine beasts but I burn up every time I get close to Goron City. Do I need an elixir or can I buy some protective clothes somewhere?
You need to buy women clothes to get in Gerudo City, it also helps to survive the dessert. Where can you get this there is a guy on a roof in Kara Kara Bazaar. Talk with the poeple arround there and you will find him
Before going to the city at the beginning of the zone visit the stables. A girl outside will be selling fireproof elixirs, i suggest taking 2-3 and just sprinting to the city. In the city buy fireproof legs and you will need one more set piece to be able to get to divine beast. u can buy the whole set or u can do a quest for armor in the first mine u pass.