I know that there is such a thing as absolute zero where
the particles can't get any colder, but is there such a thing where the
particles can't get any hotter?
Not really. Temperature is a measure of average kinetic energy of the
particles, and the minimum value of kinetic energy is zero. There is no
maximum value, however.
Richard Barrans Jr., Ph.D.
The other limit would be infinite temperature. This is not as
crazy as it sounds. Temperature is formally a measure of the
probability of a system being in states of different energy, e.g. the
fact that the Earth's atmosphere has a temperature of 300 K (roughly)
tells you how much less likely it is for a nitrogen molecule to be at
10,000 feet altitude (where it has significant gravitational potential
energy) versus zero altitude (where it has none).
Zero temperature means formally that the system can ONLY be in the
lowest possible energy state: in our example, every nitrogen atom must
be on the ground. Infinite temperature means that the system can be
found with equal probability in all possible energy states, including
those that have infinite energy: in our example, nitrogen atoms are
equally likely to be at zero altitude as halfway to the Moon.
Dr. C grayce
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Update: June 2012