Wearing a suit in the desert without breaking a sweat

Yes. Go in Winter.

Deserts aren't always hot. They're just very very dry.

Exactly right. In fact Mongolian deserts can be -30C to -40C below in Winter.

Can't watch the video from work, but in extremely hot places a light-coloured linen suit, or at least trousers and a long-sleeve shirt, would be better than shorts and a t-shirt. You need to keep your skin covered or it will burn. This is one of the reasons that most desert-dwelling peoples wear full-length robes, and why I don't understand when some people on this forum try to argue that where they live it gets so hot they need to wear shorts.

I just tried explaining this to people at a Memorial Day BBQ, how I was fine in my long sleeve seersucker shirt and linen pants while they were sweating away in shorts and a tshirt.

I'd imagine his trailer was air conditioned. And it seems the shots of him walking away were shot at dusk.

You're body also adapts after awhile. During the summer here will hit the 40sC some days. It'll then drop into the high 20sC over night. You actually feel the need for a sweater at night