My partner is up there for a short stint and I had the chance to ride around...during the heatwave.
My advice is - don't visit the desert in the height of summer. My goodness it was hot. Not a single day was under 40 degrees! Luckily this sort of weather doesn't last for long. The evenings are rather cool - lack of humidity means that as soon as the sun gets low the heat dissapates quite quickly. Sun exposure is not an issue as you ride really early or rather late.
But that is only in the summer. Winter, apparently, is quite nice
Alice Springs breath takingly beautiful. And there are heaps of trails. It is worth the visit. If you are not riding the DH tracks you can get away with a hard tail, but a XC dual sus is nice.
There are a lot of mega bindis - supersized bindis that get into everything. Down your socks and into the waist band of your pants. The thorns are sharp and you can't ignore them. People ride around with those green gardener's over sock/shoe thingys.
Take a puncture repair kit - you'll be doing this a lot. There are plenty of thorns and broken glass around town. You can go tubeless but this only staves off the pain for a bit longer. In my 5 days I saw 3 tubeless tubes get punctures. They do a sort of tubeless tube thingy now (a tubeless tyre with a gooey tube).
Take a GPS also. If you are not a local it is easy to get lost. Once you are over the hill, you can't see the town anymore - who knows where you are at? I got so turned around I couldn't figure it out.
The Rough Riders club is awesomely social. They pull a big crowd for social rides on wednesdays and weekends - even on the hottest days there were over 10 people for a ride! Try to hook up with them.