Is there an absolute maximum temperature?

This week we find out about the inequality of the temperature scale as a listener asks: "If we can have a lower limit on temperature - absolute zero - so cold that nothing happens, why do we not have an upper limit - a temperature that is so hot that atoms and particles are so hot that they are ripped into the most elementary units and become so excited that they cannot react with anything around them?" Plus we wonder why we don't always get our priorities right........