Depends what kind of dessert environment. If sand dunes and similar terrain that would be difficult terrain for most humanoids, perhaps they are adapted to moving along sandy environs and do not get disadvantage.
They should be adapted to conserve and need less water. Admittedly this is a less interesting skill in combat. But it can be useful narratively, think of the the Texas-ranger protagonists in The Lonesome Dove, who give up their chase of Blue Duck, because they know were out of water and they knew that he could go without water longer than they could
Some other interesting behavior and adaptions for kobolds, based on real-life animals:
1. They should be crepuscular or nocturnal. In US deserts, most reptiles and many snakes are crepuscular. Seem to be more snakes than lizards that are nocturnal.
2. They should plug the entrances of their burrows/lairs to keep out the heat. This can be a stone rolled over it, covering with vegetation, or a door, depending on level of technology/civilization.
3. Some animals hibernate in through the hottest periods. Kinda boring adventure wise, perhaps. Perhaps, if things go real bad for them, they can cacoon themselves inside a water-soluble mucus sack and hibernate until it rains.
4. Heat dissipation. Desert animals have evolved a number of way to become more efficient at dissipating heat from their bodies. Longer appendages, lighter colors, and urinating on themselves. Lanky, light-colored kobolds that piss on each other to keep cool, could be fun.
5. Water retention. Reptiles and birds excrete metabolic wastes in the form of uric acid, an insoluble white compound, wasting very little water in the process. Most stay underground during the hottest periods of the day.
6. Acquiring water. Probably from succulent plants like cacti and from other animals they eat. As intelligent creatures they probably have development methods to collect (solar sills, wells) and store water. Some creatures like certain desert rats can metabolically create their own water from dry seeds, which is pretty amazing.
7. Maybe they are spiky because their ancestors, like the horny devil developed spikes that collect dew and trickle it to their mouths. That could lead to "civilized" behavior that takes advantage of this adaption, like drinking the blood of sacrifices buy drippling it onto their heads and letting it trickle to their mouths.
8. They may have long and wide tails that they can curl over their heads giving them shade.
9. Or instead of shade tails, maybe, like Gila monster, they store fat in their tail, allowing them to go months between meals. Healthy, well-fed desert kobolds could have large, thick, club-like tails that could be used for an extra attack.
