Interesting article about the Phoenix issue in Wired: [www.wired.com]

PHX has had this problem before. It gets too hot, and some planes can't carry a useful load and still take off. In this case, apparently, all the cancelled flights used CRJ regional jets, which have a maximum certified operating temp of 118F. Larger Boeing/Airbus models are rated for operation into the mid-120s. Those ratings are included in operating manual charts. Near the top end of those charts, some adjustments in load are necessary; beyond the top, a useful and safe load can no longer be carried, and operating there is illegal under the federal aviation regs since the aircraft would be operating outside its certified limits.

With a long enough runway, you might theoretically be able to go faster and still take off, if the tires hold up at the higher speed. PHX' runway is about 11K ft. long; good sized, but nowhere near Denver's 14K. There are also safety rules about how much runway can be used, so if something goes wrong you can abort the takeoff without running out of runway; commercial flights don't violate those rules, and I think you would agree with them if you're riding the plane.

As with many railroad rules, aircraft rules are based on laws of physics and people or things getting hurt. They're not somebody arbitrarily messing around.