I use a 2011 Mac mini (2.3 GHz model) with a 27" Apple Cinema Display (2560x1440) without any problem.
the way to test this would be to use some intensive apps...
could you try using Netflix or Lovefilm for 10mins full screen and check how the heat and fan's responds?
Microsoft Silverlight is a hog.. i know on a 27" imac 2011 it works fine but a mini mac would be interesting.
i have a 13" MBP 2011, thunderbolt display connect and my fan and heat reaches 5400rpm 80 degree celsius
would appreciate it!