Not sure where you guys get these things from buy I have never heard of a router overheating. Also I doubt the firmware would cause the connection to drop. What you might want to do is try recycling the modem and router. Also make sure the issue is not with the modem itself. Check the logs of the modem or call up comcast and ask them to look at the history to see if they notice anything. They can run line checks.
I get it from experience. Anything can overheat, when routers overheat they drop connection. It was an issue with the older linksys routers, because the internal fans would fail. I haven't heard of any issues with the newer ones, but if it's in a closet with a bunch of other electronics it's possible. Recycling the modem and router is fine if you only have to do it every once in a while, but if you have to do it everyday, then there is another problem.
Here is another possible fix I found with a quick search on the linksys forums.
Open the router's setup page and Under the Setup tab,Make sure that the "Keep Alive" option should be checked.Also,change the MTU value to 1400.Power Cycle the router and check.