Unclassified (physics): JEE Advanced 2019 Physics question

A current carrying wire heats a metal rod. The wire provides a constant power $(P)$ to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature $(T)$ in the metal rod changes with time $(t)$ as \[ T(t)=T_{0}\left(1+\beta t^{\frac{1}{4}}\right) \] where $\beta$ is a constant with appropriate dimension while $T_{0}$ is a constant with dimension of temperature. The heat capacity of the metal is,