Why are some flights cancelled during extreme heat waves and not others?

Whether an aircraft can fly in extreme heat depends on a number of variables such as type of aircraft, load, airport elevation, runway length, and topography in the vicinity of the airport, etc. In the simplest terms, extremely hot air is less dense which reduces the engine output and increases the length of runway needed for take-off. With the safety of the traveling public their top priority airlines operate with an abundance of caution. If the aircraft is an older model where the thrust/weight ratio isn’t as advanced as in the newest planes, or the airport is at a higher elevation where the air is thinner anyway, or the location requires a quick climb-out in order to avoid nearby building or mountains, then adding extreme heat can tip the “go/no go” decision in favor of cancellation. As a very general rule, the smaller aircraft used on the regional subsidiaries (i.e. United Express, American Eagle, etc.) of the major airlines are the most often cancelled.