I lived in Dhahran / Al-Khobar for 8 years and feel my time there raised the bar for my heat/humidity tolerance. I'd frequently go on 2 hour mountain bike rides in 117-120 degree measured heat with 70-80% humidity.
Our bicycling club would ride at night during the week (when temps would drop to a chilly 104-105F) or at 5AM on the weekends (the sun rises at 3:30-4 AM in Summer).

Mid-July through September are the worst months, as the intense humidity that is generated by the shallow, hot Gulf (98F water temp by late summer) is at its peak.

I spent about a year of my time in Saudi in the desert, which had no humidity issues, and was comfortable riding in temps up to 125F (50C). I did venture out a few times on 55C days (130+).

Despite the time there, and having grown up in Austin, I REALLY dislike humidity. I can handle heat, but far prefer to ride when it is 65-75F.