Does cooking one month expired canned goods render it edible?
If the food is spoiled, no, it's still unsafe, because cooking may not destroy toxins that have built up over time.  Botulism is a particularly nasty one that will not be destroyed without pressure cooking, and can really, really mess you up.

... but in the case of canned goods, if the cans are still intact (no punctures, rust, etc), and the canning process was done correctly, the food inside will remain safe even if the quality of the food may have changed, which is what the 'use by' or 'best buy' dates typically signify for canned goods.  (some will argue it may change for the better).  

In the scope of storage lifetime for canned goods, one month is relatively nothing.  It's more significant what temperature it had been stored at up until now, as canned goods age significantly faster at warmer temperatures.  I personally wouldn't hesitate to eat stuff in a one-month past 'use by' date can (or even a year past), but I'm in a more moderate climate than you are.

If the cans have been in a relatively cool place (not in direct sunlight, or stored near a heat source), it's probably okay.  Look for obvious signs of puffiness, and listen for air escaping then you open the can  (entering is okay ... escaping is bad).  If you hear lots of hissing after breaking the seal on the can or if it smells or looks off, just pitch it and don't risk it. (as would be true for canned goods still within their 'best by' date ... although then you might be able to get a refund from the company if you contact them)

And, to cover myself from potential litigious behavior : If you're immune supressed, I wouldn't suggest you take the risk.  I also wouldn't suggest serving it to others ... although the risk may be low, other people should get to make an informed choice if they wish to risk it.  (older people and small children are more likely to have issues)