Temperature of the back of a turbine jet engine (or something like that)

There is an extremely wide range - could you be more specific as to what type and under what operating conditions?

 

There is a pretty good introductory treatment of the different types of jet engines at wikipedia.org:

http://en.wikipedia.org/wiki/Jet_engine

As Russ says, and as the article discusses, different jet engine types have different exhaust temperatures. High-bypass designs obviously cool off the exhaust more than low-bypass types. The temperature of the combustion is given about 2/3 of the way down the long page.