You warm up the air on the way out to expand it and you get more air to spin the turbine. More bang for your buck.
I believe is the thinking.
The real masterstroke here might then be to put this system in an area with large diurnal temp changes like the desert, then charge this system with cool night air, and then reheat it and generate electricity during the day with warm daytime air. Heat pumps could be used to nudge the temp on either end into it's optimal range.
It then becomes a solar thermal hybrid compressed air energy storage.
This could pair well with renewables that are more available at night like onshore wind.
I was 17 at the time, and I have been into some of the most incredible caves - the best in Ganung Mulu National Park in Borneo Malaysia...
As the rains flowed out and carried the guano from 5 million bats into the forest to fertilize it...
And then I realized it wasnt just the desert - it was the caves...
Caves (giant ones) are really important for planet health.