I guess that if you stick your finger into the water it will still get burned, am I wrong?

Only if you're silly enough to stick in your finger at the wrong moment.

Ok, I thik we have a problem of definition here. You said the water got colder in a thermodynamic definition. But you agree that if I take a thermometer and insert it into the water and leave it there for a while it will still indicate 'hot water'. Right?

What I don't understand is your thermodynamic definition of colder. And I'm no physicist. Btw, I understand that with the information about the velocities you have power to make the water colder, but that doesn't mean that it actually will get colder(at least not right now).