The single biggest problem that I see with your model is food.
Not all deserts are hot. Take Antarctica, for instance. Almost no precipitation. You have access to water there, but it's either locked in ice or it's salty (from the ocean) Also (most importantly) nothing grows there.
The species you're describing is almost the reverse of a penguin. Antarctica gets a lot of breeding colonies of penguins because of the absence of predators. Interestingly enough, Flamingos do something similar, nesting in soda lakes because the caustic nature of the lake means no natural predators. In each case, you either need to find food (and water) you can process in that location (be the local apex predator) or you need to venture out of that environment to find yourself (and in the case of penguins, your family) sufficient sustenance.
Your species would probably do exactly the same thing. Being able to live in the middle of a desert means that you'd have major towns out there for things like breeding and security, but the food and water issue would have to be resolved. This is not so much an issue if you have an active trader culture as getting resources to and from the towns wouldn't be any larger a problem than it is for us today (How much food actually gets grown in New York, for example?). But, your people need something to trade for it. What is their industry?
Personally, I'd go for glass manufacture. You already live around heaps of sand, you're less susceptible to heat stress and it's a commodity that would be in high demand in your world.
So; with that in mind, your culture is very protective of its young. Most other species have probably never seen a young member of your species. They're artistic in nature, and have a canny sense for trade.
They're curious, insightful, and probably more technologists than spiritualists. That is not to say that they wouldn't have religious proclivities, it just means that as a whole, their creativity is primarily directed to industry because without that, they would have to risk the safety of their children to migrate closer to food sources. Also, good trading ability means that their math skills would grow, and that also helps them with things like science and technology.
All this said; they lack the natural resources that we take for granted. They're not in mountains (so lack the experience that leads to metallurgy), there'd be no practical reason to engage in mining for that reason as well, they don't have access to wood, bone, or even much stone which would lead to the creative resourcefulness that we assume a group like this would need. This is all the more reason why they would have a technology that focuses on the production of glass; it's the one thing they can manufacture in abundance and you'd probably find that they'd have built an entire culture and technology around it. Glass huts, even.
This is a group that would by definition probably be both culturally and technologically narrow until they had regular contact with other species, not because they are unintelligent, but because their intelligence hasn't been exposed to other environments where it can be expanded on a regular basis.
The key thing to state in summary about your species is that this specialisation they have (if you look at penguins, flamingos and others with similar traits) would be used to evade predators and enemies in the first instance and any other consideration (even the ones I list in this answer) are largely speculation.