Temperature is to do with the movement of molecules.
At any temperature where Caesium is still Caesium, those hyperfine levels internal to Caesium won’t change.
Analogy: no matter how fast you drive your car, the distance between your pedals doesn’t change. Unless you crash the car :0)
Or unless you skid sideways at an appreciable fraction of the speed of light ... in which case the pedals would get closer together, as measured by an observer.