Find the relationship for how the temperature distribution changes with time with respect the un-deformed rod and the deforming rod.

Lets say you were interest in looking at temperature distribution as a rod deforms. You have found the point map for the rod:
x = (1 + t)X
As well as the distribution of temperature in the Lagrangian description.
T = Xt^2
Find the relationship for how the temperature distribution changes with time with respect the un-deformed rod and the deforming rod.

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