These days in Yazd the average warmest temperature in July is 40 degrees, so if what you're saying is correct they'd be able to cool it down to a liveable 30 degrees even in the warmest part of the day. And at night temperatures still dip to 26, so the indoors temperature probably wouldn't quite reach 40 even without this system. So it might make the difference between 40 degrees outdoors and high 20s indoors, which is fantastic.
Would be interesting to know if average temperatures got up to 40 in the summer around the time they were built as well, or if average temperatures in the region have been rising.