Sorry to be the bearer of bad news but I suspect that the other posters may be unwittingly leading you away from what I strongly suspect is the root of your problem - Click
here to see the countless numbers of people who have experienced problems such as yours. I personally know 3 people who have independently experienced the problem themselves and either had intermittent or total failures.
It is entirely likely that the recent hot snap may have contributed to an exacerbation of your symptoms. In the meanwhile, you could try standing the router upright, moving it out of direct sunlight and putting a fan next to it or some other crude cooling that may be enough to keep it operational.
Personally, I'd just buy a Linksys - it might not look all Apple and trendy but it does what it says on the tin. Good luck.