Is it permissible for someone who performed tayammum due to intense cold at work to continue praying with that tayammum upon returning home, or must they perform ghusl?

Tayammum (dry ablution) is not sufficient for the obligatory ghusl (full ritual bath) when water is available, except in the case of being unable to use it due to extreme cold that cannot be endured, coupled with the inability to heat the water. If hot water is available, tayammum is not permissible. However, if it is impossible to heat cold water and you are unable to perform ghusl with it, then there is no harm in performing tayammum and praying. Whenever it becomes possible to use water, even by heating it, ghusl and wudu (ablution) become obligatory for all subsequent prayers.