I enjoy using the "how quickly does it cause burns" method of measuring temperature, but only for things <50°C. Hotter things call for a cheap infrared thermometer.
I really have no idea how hot my exhaust is when I'm pushing the car hard, but after driving gently around town, shutting off the engine, and popping the hood, I've seen 350°C at the catalytic converter. It's probably a few hundred degrees higher during a highway hill climb.
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