temperature going up to redline in 2006 S
So I recently just bought a 2006 MINI cooper S (as in recent I mean just paid my first car payment yesterday). I am loving this car, but I have been having a bit of trouble with the coolant system. I noticed the other day that the temperature went to redline when I parked my car. I looked at the coolant the next morning and it was extremely low. I took it to precision tune and had the coolant flushed and refilled and they kept it overnight for leaks and weren't able to find any. I took it home and all was well until I was driving home tonight and even with it being cool out the temperature went almost to redline when I was driving (before it was only in idle and parked). I am so confused as to what this problem may be and I am really hoping its nothing serious. The fan was kicking on high before when the car was off for about 30 seconds to cool it down so I'm not really thinking that. I filled up the coolant and had that taken care of...so any ideas? I am new to MINI and a car dummy and I really am not looking to pay any expensive repairs on my first new(ish) car.