Higher altitude = lower pressure = lower air density = less thrust.
Higher temperature = lower air density = less thrust.
That' s what is referred to as hot & high.
But flex take-off has nothing to do with hot & high.
Outside air temperature affects the TIT (turbine inlet temperature).
For a given setting, the higher the temperature of the air that comes into the engine, the higher the temperature at the entrance of the turbine.
The turbine has to bear with alot of heat from the combustion chamber.
The material it is made of has a given life limit with exposure to these high temps but also very differing life limits for different temperatures.
To give you an approximative example, a turbine exposed to a 1600°C could do 2000 cycles when a turbine exposed to a 1500°C could do 2500 cycles.
By reducing only a few % on the take-off thrust setting you can save alot on cycles.
By flexing a take-off, you can create a margin that helps you save the turbines from being exposed to higher temperatures, significantly increasing its life expectancy.
If you have hot and high conditions, you don' t flex.
You can' t because this is where you need the additional thrust that is going to eat up on your turbine cycles.
If it' s cold and you have some margin to play with, you can flex and save cycles on your turbine.
That simple.