I am indeed the lord of all deserts.

And you exaggerate the growth of the Sahara. I can assure you that it was quite large 2000 years ago. Oases weren't that common in the deep Sahara anyway.

Even if you could reach Terhazza, morale penalties would not be worth crap. You would still beat the three-unit army defending the city with 0 losses.
SOMEHOW, your army of, say, ten thousand apparently immortal soldiers suffered not a single casualty in the long desert trek which should have reduced the force to a few hundred, even if they managed to reach Terhazza in the first place (knowing the exact location of everything is unfair).