Was your check engine light on when you went into the dealer? It could be that they cleared the faults, but I'd assume you'd have a CEL on for a thermostat issue. Thermostats, when leaking, do not have to show signs of leakage on the ground. They can seep/leak and the liquid can get burnt off before reaching the ground. Seeping wont show up on the ground until it acquires into a drip. Does the vehicle gauge on the cluster show any signs of overheating? I'd ask the dealer exactly what they saw that lead them to believe you have a t-stat issue. Otherwise, I'd take it to a MINI indy shop for a second opinion. It could be they're recommending it due to the age of your MINI. However, it's a part that people typically don't replace until it is not functioning right. Some replace for preventative measures, before any signs of it being faulty.
If there are absolutely no sigs pointing to a thermostat issue, you could leave it be or get a second opinion. MINI indy shops tend to be more truthful about service repairs. Can track one down in your area by plugging in your postal code here:
Mini Cooper Repair Shops - Find a Mini Cooper Mechanic | MiniRepairShops.