To be more specific, how did both sides in the Africa Campaign not get cooked alive in their mostly metal tanks.
Open the hatch, drive forward, hope the air circulates a bit.
In some vehicles, the air could be drawn into the engine through the crew compartment, which meant that there was a constant flow of, granted, hot air. It also meant misery in Winter.
I'm not being flippant, by the way, with the answer. It's possible to survive quite well, if uncomfortably, in a tank in the desert with no air conditioning. Just ask any modern Abrams tanker who went to Iraq. (Like me!). You sweat a lot, and drink a lot of water, but that's as far as it goes. Only the very latest generation of tanks, which hadn't filtered down to me by six years ago has what is known as the "thermal management system", but really, that's just to keep the electronics cool.