Very high temperatures limit how much payload and/or fuel you can load on a plane.
To help you visualize it, in hot air the air molecules are more energetic, which means the engine will have hard time compressing hot air vs. cool air. Losing thrust.
Hot air—with the molecules spaced farther apart—has less density, which reduces the lift capability of wings.
Hot and High
Vegas is not only hot, but also high, which means the air pressure is already less than at sea-level.
Each plane has its own performance charts, and on each flight, the flight dispatcher and crew make sure the weather, elevation, etc., would allow a safe take-off and climb.
A plane is configurable for such changing elements. For example using higher thrust setting, or more flaps to augment the lift.
If you have a very heavy plane, hot and high situation, and a short runway, then things become very marginal—
—not just for the take-off run, but also in case of an engine out during take-off, i.e., losing an engine. The plane still has to be able to climb.
That's why in places like Ethiopia, South Africa, Australia, etc., airlines preferred1 quad-jet planes over twin-jet planes. To have bigger margin of safety in hot and/or high operations, i.e., to be allowed to carry heavier loads.
1 When tri/quad-jets were commonly offered alongside ETOPS twin-jets of same class.
Example of Impact
(Map generated using Great Circle Mapper)
A cargo MD-11 plane taking off from Ethiopia en-route to Europe can't take off fully fueled, and has to stop in Cairo for a re-fuel. Note that if Ethiopia were at sea-level or cooler, a direct flight would have been possible.
For landing in a hot and/or high airport, the landing speed will be higher, so what matters is the runway length available for landing. Again there are performance tables for that.
Rest assured, those things are checked and double checked. And no one can tamper with reported weather, because it is very critical to flight safety.
Also, planes do have their own temperature sensors. Newer planes can even alert the crew if the gross-weight, configuration, runway length, temperature, and elevation combo isn't sufficient.