What year/model R56 do you have? How did they come to this conclusion if there were not faults thrown for the thermostat? Why were you in the dealer (i.e. oil change, check engine light, etc.?) If there was no fault it makes me believe that they saw it leaking. You can get into it and inspect to see if you see any coolant coming from it. Is your vehicle overheating? You can plug into your OBDII and watch your temp. It should read about 220F at operating temperature. If it's below, let's say around 190F, you could have an issue, but I'd think a fault code would be present.
Depending on if it's a Cooper or Cooper S, and its year, this article here can help you find the location of the thermostat to inspect it:
MINI Cooper R56 Turbocharged Engine Thermostat Replacement (2007-2011) | Pelican Parts DIY Maintenance Article.