If not, has anyone ever measured how hot they get?

They’re nowhere near hot enough for combustion.
Skin burns however………….

burned my leg on one which left a near perfect inprint of the rotor on my calf

mine turned purple on a massive descent in andorra one year

As a disc newbie, years ago, I got a nice disc rotor burn on my forearm when picking the bike up by forks and seat tube to put it on the car bike rack as soon as I pulled into the car park at the bottom of a steep hill!

mates went blue on last weeks descent 😆

What size disk for lightly grilled pinkies?

us blokes are talkin about our dics turning blue and purple

I melted a hole in some shorts a few years ago,

1st proper go with a proper bike in Morzine 10+ years ago I go to straighten the bars after a crash and end up with Hayes written on my calf for a month.

Never set fire to anything but I don’t put the bike down disc side first in summer here in Oz, too much tinder dry stuff out there.