And... this isn't a puzzle as such but you could turn it into a competition question for the students. It's a 'factoid' that still makes my brain ache at the unimaginable scale of it...

If the coldest temperature is absolute zero. What's the hottest temperature?

(From the BBC's Dr Chris Smith and the naked scientists – 26 March 2012.)

Answered by Sam Gregson, high energy particle physicist at the University of Cambridge and working at the Large Hadron Collider in Cern, Switzerland.

"The temperature of a system is simply related to the amount of energy in a system. Because a system can't have a negative energy there is only so much heat you can remove from it and so a limit to how cold you can actually get. This is called absolute zero. We have got very close to it.

Scientists in Finland have cooled rhodium atoms to a 10th of a billionth of a degree above absolute zero.

On the other hand an absolute maximum temperature would require there to be a limit to the amount of energy you could give to a particle and as far as we know there is no such limit.

Although the speed of light is the universal speed limit the reason you can't get there is that this would require an infinite amount of energy. So this speed limit does not limit the amount of energy and therefore the temperature of an individual particle.

The most energetic particle ever observed was a cosmic ray over Utah travelling at 99.99999999985% of the speed of light, probably a single proton, with about 50 J of energy.

This is equivalent to about 5,000,000,000,000,000,000,000,000 (trillion trillion) degrees Celsius. And there is no evidence that this is the hottest you could get to.