Further tests are getting more and more interesting.
I took a rubber band (untapered) and stretched the middle part out, then waited until it had cooled down.
Then I relaxed it.
It was COLDER than the room temperature! The first pic shows the retracted band between my hands, the second one the whole band (with the ends beeing warmed from my hands).
This means that you can - in theory - build a fridge (or an air condition) with rubber. Take a slingshot outside, draw it out, wait about 20 seconds, then go with the stretched band back into the house, and let go.
You can build a "Sterling cooler" with this, except that a Sterling normally uses gas and not rubber...