Are there organisms which have compartments of different body temperature?
For most of the multicellular organism; different part of body would exist in  different temperature; however there are more extreme/ drastic examples too. 

Bombardier beetles; a group of beetles; that have a specialized reaction chamber in the body; where they can produce a hot and noxious reaction-mixture. They project it towards the enemy; and can throw by bending their pygidial region to wide range of directions. They do it as a defense mechanism. 

 

Wikipedia image of bombardier beetle. They are some members from the tribes  Brachinini, Paussini, Ozaenini, Metriini of family Carabidae. 

The reaction mixture can attain a temperature up to 100&deg;C , more than enough to cause thermal death of normal protoplasm. But the reaction take place in a specialized compartment inside their body... and nothing else happen to the life of the beetle. 

Here are some image of the anatomy of bombardier beetles (from here)

pygidial glands within a Bombardier Beetle; highly diagrammatic. 

 more detailed diagram of the gland, however, diagrammatic. 

 this is a more realistic diagram of the gland in bombardier-type carabid beetles; whole diagram showing forms of this glands in other-type carabid beetles  is available in the main website. 

This paper includes a simplified diagram of chemical reaction in the chamber. reaction summary.

Here is an image from BBC showing bombardier beetle in action.


  Reference: Wikipedia