HEY GUYS new to the form i have a quick question , i have a 2010 cooper s that i have had since march with only 25,000 miles on it . i was on the way home the other day and it just died so i call the road side assistance they sent out a guy with gas , it took him about an hour to get there , i told him it had gas in it but we put it in anyway and the car started . then the next day i was driving home from work and it did it again so i call them again to send a tow truck well it took 4.5 hours for the tow truck to get there and when i meet him out there to pick up the car it started , seems that when it gets hot it does this and when it cools down it will start up , any body else ever have this happen. THANKS

Used to be a thing on older cars when the ignition coil was starting to break down or the distributor condenser was on its way out, car cut out when hot and then ok once cooled.
But the new cars like the MINI have the coil on each spark plug? and I doubt whether they have a condenser like the old distributor cars had.

After it died did it try to turn over and just wouldn't start...as if it isn't getting gas?

Could it be possible that the gas tank is not venting properly and is building up a vacuum hence stopping the flow? Opening the cap will release the pressure and the flow will start again. May be worth a try if it does it again.