just saw this thread. I think my first router died of heat stroke.
My replacement has done the same thing where it would lock up, give me no internet, but say i was connected just fine.
So i DIY'd a 120mm fan powered off a 12v ac adaptor underneath it. Runs MUCH cooler just based off of touching it. Has not become unstable again.
For what its worth the manual lists this as the operating temp range.
Operating Temperature
• 30ºto 104º F (0ºto 40º C)