Unfortunately there is no surefire way to pick up a fever immediately. All the things people recommend against- going outside with wet hair, wearing damp socks etc. They are all old wives tales and will not make you instantly sick.
Also, I would strongly advise against it!
Getting sick at anytime is unfortunate, but getting sick because of something you've done to yourself is crazy - and could be a little dangerous, too.
Have you thought about trying the thermometer on the lightbulb trick to make it look as though you have a temperature?
Be careful about getting it too high though or your parents might rush you to hospital thinking you're on the verge of death....
If I need to get out of something I usually say I have a migraine, which is essentially a really intense headache (with sensitivity to bright lights). Works every time!
The other option - and you probably won't like this- is to just man up and go to school, and face whatever it is you're dreading. If it's a test or some homework you haven't done, don't worry, it'll blow over. If it's something more serious, you should maybe consider talking to someone about it rather than trying to avoid it.
(Or, if you want some tips from the master, watch this!)