Problems with my mini cooper... please help!?

i have a mini cooper convertible 2007. the fan in the car is constantly going off and keeps going for about 5 minutes after i turn it off. as well as that the car is overheating when it's on and stationary but will cool back down again when i drive. i have took it to a mechanic who reckons the water pump needs replaced but i have been told by others the coolant system might need bled or a thermostat may need replaced. i don't want to be ripped off so any ideas what the problem might be?