Why wouldn't someone wear tear-resistant, puncture-resistant, light armor in a desert wasteland?
Deserts do present a problem. For example, we learn...
Because of the climate, very little armor was ever worn in Africa. In Egypt's Old and Middle Kingdom, Egyptian soldiers never wore armor. In the Old Kingdom they are usually depicted wearing only a belt and a small triangular loincloth. During the Middle Kingdom, their apparel was invariably the same short linen kilt as that worn by civilian workmen. Hence, from the late Predynastic Period to the Middle Kingdom, Egyptian soldiers at best only wore an occasional band of webbing across the shoulders and chest.
Sometimes broad leather bands covered part of the torso of charioteers, but generally soldiers are depicted without any body protection. Again the pharaohs were, not surprisingly, the exception. Ramesses II fighting as a charioteer was portrayed wearing scale armor with sleeves, covering the whole torso. The scales were bronze, attached through holes to a skirt. His legs were of course protected by the chariot. However, even he is not always shown wearing armor. It might be presumed that other charioteers who could afford the expensive armor might also have worn it. Yet, even pharaohs, though they almost always are depicted wearing the blue crown, did not always wear armor. For example, portrayals of Seti I clearly show him without any body armor in battle. (Source, emphasis mine.)
It's true that deserts can be cold at night, but only high altitude or polar deserts are cold during the day. Death Valley would be an uncomfortable place to wear a black leather jacket and blue jeans (unless you're Mel Gibson!). But Ramesses II wore bronze scale mail for a reason — getting hurt is inconvenient.
But for some other reasons, let's look at our brothers, the Bedouin. They often wear neck-to-wrist and neck-to-ankle clothing. Why? Because even the darkest skin can burn. While they often wear white clothing, their outer robes are often colored and frequently dark. It may seem counter intuitive, but thick and black is better in a desert.
We have therefore investigated whether black robes help the Bedouins to minimise solar heat loads in a hot desert. This seemed possible because experiments have shown that white hair on cattle and white feathers on pigeons permit greater penetration of short-wave radiation to the skin than black. In fact, more heat flowed inward through white pigeon plumage than through black when both were exposed to simulated solar radiation at wind speeds greater than 3 m/s. We report here that the amount of heat gained by a Bedouin exposed to the hot desert is the same whether he wears a black or a white robe. The additional heat absorbed by the black robe was lost before it reached the skin. (Source)
What researchers discovered is that while black-and-thin makes you hotter, black-and-thick makes you cooler. The black blocks heat better when there's a wind and thicker clothes mean the heat can't penetrate as far, protecting the skin.
Is this magic? Nope. You'll notice the Bedouin clothes are very loose. You still need to wick the sweat off the body and let it evaporate or you boil in your own sauce. That's where the leather jacket is a bit of a turn-off. You'd need at the very least a really good cotton undershirt.
But you're in luck, denim's actually pretty good at wicking away and evaporating sweat.
Avoid cuts and scrapes from living in a region predominantly filled with rocks, sand, and thorny-bitey things.
Avoid real pain from near-unstoppable punk-like-dudes who are desperate to steal your gasoline.
It really does help manage the heat process. It's a trade-off between sunburn and heat-stroke.
And to top it all off, blue jeans and black leather has been the magnet-of-choice for guys since Marlon Brando (before he got fat). Surely there's a date night in your character's future?