to check it remove it and place in hot water and see if it opens, if your removing it you might aswell replace it though and then its done. to remove it, drain the rad and coolant system, theres two bolts to undo on the stat housing remove the pipe and pop the stat out, insert new stat and reverse proceedure, theres a guide in the how too.
First time its a right PITA, but as with everything once youve done it once its a breeze the next time, first time it took me a hour and a half in the middle of the day, second time it took me 20 mins at 10pm at night.