Microlight types
Don't bother thinking about Jabiru engined trikes, or for that matter any other pusher. They don't cool well in a pusher configuration, and you obviously need that capability. Plus, for hot-high you want a fair bit of thrust, so I'd look at a Rotax 912 or 912s, which will give rather more power than the Jabiru (whatever the data sheets say).
The 912 is an incredibly rugged and reliable engine, with the advantage that it can be configured with both radiator and oil cooler, which should adequately meet your needs.
Good trikes... Mainair Blade 912 and 912s heavy to fly but ignores turbulence, reasonably good cruise, and reasonably agricultural so easy to care for. It's main UK competitor is the Quantum 912, lighter to fly, responds more to turbulence, a bit more refined. There's a similar French equivalent with slightly better lifting capacity but otherwise much the same to fly as the Quantum, which is the Air Creation Buggy with KISS-450 wing.
If you want something a bit faster and have enough (500m+ in a hot-high environment) runway to allow for it there are two other British trikes, both fairly refined and with a fastish (60-70kn as opposed to 45-55kn for the Blade and Quantum) cruise, again both using 912 variant powerplants. One is the new Pegasus Quik - which is pretty much cutting edge at the moment, the other is the Raven (EclipseR) 912. The latter is better in turbulent / thermic conditions as well as being a few grand cheaper, the former is much more refined with a better speed range.
Pretty much all these modern high performance trikes cost around UK£20, but if you are on a budget most of the manufacturers will have a 2-stroke (Rotax 503-2V or 582) equivalent for around £12-£16k.
3-axis. I'm guessing you want shortish field, good lifting capability, and 2-place dual controls. I'd also suggest you want to avoid fabric coverings in the desert since they'll UV degrade chronically and aren't as easy to bag-up and store out of the sun as a trike. For the same (UV degredation) reasons I'd have thought avoiding composites would be a sound move.
Try the Czech Aircraft Works Zenair CH701 (or the Italian ICP MXP740 Savannah which is basically a direct copy) for 912 or Jabiru engined STOL capability at £20-£30k. For a bit more cruise performance at around £30k but less STOL two Czech aeroplanes, the Eurostar or the Czech Aircraft Works Zenair CH601 should both give you nice touring (80kn) aeroplanes that'll operate happily in the hot/high environment from a 700-1000m runway quite happily.
One exception to what I said, is the X'Air, an easy to fly, slow, dirt-cheap Indian tube and fabric aeroplane. Buy them direct from Raj-Hamsa in India and you should be paying under £10k per flying aeroplane. Go for the Rotax 582 engine and C or E type gearbox + a decent (3.47 or 4) gearset to keep the propeller tipspeeds down. Expect to scrap the engine and sails every 600 hours or so in that environment, but at about £3000 for engine and sails together that's not too bad per hour. Alterntively the 2.2 litre Jabiru seems to work well on that airframe so long as you pitch the prop to keep the RPM constantly below 3000. Personally I wouldn't both with a 912 on an X'Air it doesn't need the power and won't go much faster, or with the newer X'Air F, the flaps are totally unnecessary.
That help at-all?
P