Personally I think the "too hot" story was just an excuse from a captain who did not care to go into a long complicated explanation, or explain a company decision that would have gotten angry letters from passengers.
That said, it can be "too hot" to land at a given airport.
Heat affects aircraft performance adversely. You cannot begin a landing approach unless you have the performance to do a rejected landing with one engine inoperative. Not likely to be a factor at LGA
ever but it does happen at high elevation airports. Also the company might not want the plane landing there if it will not be able to take off until the weather cools down.
Also you cannot land if the ambient temperature is above 50o
C or 122o
your engines are flat-rated to that temperature. The airplane will do it, but you just don't have the charts for it.
Finally, no, the tire temperature is not going to be the limiting factor. The tires are serviced with dry nitrogen and there are fuse plugs to blow and relive the pressure if it gets too high. I'd be interested in hearing from someone who knows, approximately what kind of temps it takes to blow the fuse plugs.
Happiness is not seeing another trite Ste. Maarten photo all week long.