Any metallurgists want to weigh in on (and waving away any statement of "it's magic") the likelihood of that chain actually being far too hot from sun exposure to be touched?
Not a metallurgist either, but it's really hard to say.
We lack too much info, like how hot is it actually ? Notice that they aren't quite shown as sweating buckets despite fighting there ?
It gets really cold at night in deserts, so even if it's a really hot desert, if they are here during mornings, the chain should be at best temperate.
And as CA said just above, it depends on what the chain is even made from.