If a bacterium can survive in high temperature it's daughter cells

will generally also be able to survive in high temperature. This is because the ability to survive in high temperatures is usually encoded in the genetic material of the bacterium, which is passed on to its daughter cells during cell division. However, it is important to note that genetic mutations or changes in the environment can sometimes affect the survival capabilities of the daughter cells, so it is not guaranteed that all daughter cells will have the exact same ability to survive in high temperature as the parent bacterium.