Keep your fuel can out of the sun at all times. Cut early in the morning and try to be done with things before the major heat starts. Keep the saws real clean, air blast out the fins and whatnot. Be finicky with a sharp chain, not only does it cut better, but it will help to reduce the engine load, which in turn will make the saw run better and last longer.
Drink your water/juice whatever well in advance of feeling thirsty, and try to work or get back into the shade as much as possible, you and the saw.
I work in the heat, and so do the saws and other equipment, but I pay attention to overall heat issues and just don't push things too far.
I am not a professional cutter, and I get the impression, just from reading here, very generally, the guys who do cut at a full time pro level tend to push their equipment harder than what I would think is optimal. Under the gun to make that money or hit that work deadline, etc.
Not that that is terrible or anything, it's fully understandable, just that they expect to wear their stuff out as a cost of doing business. I would rather not push or work my tools quite that hard for the level I cut at. "Casual" or semi pro side job cutting I would think the same way, take it a lot easier in the heat, both you and equipment, and you and the equipment will last longer..