Sorry to here your having problems it could be a few things.
Firstly you need to fill and bleed the cooling system this can be a pain, but has to be done correctly take your time.
You need to use the correct coolant and not just water as water bolls at 100 deg c. the minis run around 90 to 120 deg c.
it needs to be the correct coolant Halfords sell it Halfords | Comma XStream G48 Antifreeze Concentrate 5 Litres
This is what I use in my minis and its approved for bmw just follow the mix ratio
Once this is done you need to see how fast the coolant temp comes up to operating temp.
You should be able to tell if the thermostat is opening but feeling the coolant pipes from the Rad.
If car starts getting hot quickly and the rad hoses are cold it's a good chance the thermostat is shot like the num says but could also be the water pump.
The over heating may also be because the radiator low speed and second stage fans are not cutting in to cool the coolant, so you need to check this as well when you are warming the car up.
If you know someone with a scan tool or similar you can keep an eye on the water temp and make shore the fans cut in at the correct temp, and also you can see a slight drop in temp as the thermostat opens
If the fans don't check your fuses and relays for the fans and then temp sender
If you are worried about the head gasket a hydrocarbon sniff test can be done on the coolant this will tell you if the head gasket is leaking in to the cooling system.
Hope this helps