Is there any variation in a cesium-133 atom’s frequency?

With the second defined by cesium-133, I’m curious if there is any ambiguity to the definition or if it’s a true universal constant. Ignoring the effects of relativity, if two people each take a cesium atom, will they always agree on the number of transitions the atoms made? Even if one is brought up to arbitrarily high temperatures while the other is brought to near 0 Kelvin?