The weather forecast for the US city suggests temperatures could reach 120F (49C) on Tuesday.
That is higher than the operating temperature of some planes.
American Airlines announced it was cancelling dozens of flights scheduled to take off from Sky Harbor airport during the hottest part of the day.
The local Fox News affiliate in Phoenix said the cancellations mostly affected regional flights on the smaller Bombardier CRJ airliners, which have a maximum operating temperature of about 118F (48C).
The all-time record for temperatures in Phoenix is just slightly higher, at 122F, which hit on 26 June 1990.
The cancelled flights were scheduled to take off between 15:00 and 18:00 local time.
At higher temperatures, air has a lower density - it is thinner. That lower air density reduces how much lift is generated on an aircraft's wings - a core principle in aeronautics.
That, in turn, means the aircraft's engines need to generate more thrust to get airborne.
It's a well-known problem - a 2016 report from the International Civil Aviation Organization (ICAO) even warned that higher
temperatures caused by climate change could "have severe consequences for aircraft take-off performance, where high altitudes or short runways limit the payload or even the fuel-carrying capacity".
Those problems are why many countries in the Middle East, and some high-altitude airports in South America, tend to schedule long flights for the evening or night, when it is cooler.
Phoenix flights cancelled because it's too hot for planes - BBC News