 Solution

The specific heat capacity $c$ is the energy needed per unit mass per unit increase in temperature. With $c$ constant, a small element of volume $dV$ has mass $\rho dV$ and thermal energy $\rho cTdV$, measured relative to the reference at which $T=0$. Summing over $\Omega$ givesChoosing a different reference temperature only adds a time-independent constant to this energy, so it does not affect the heat balance with volumetric heat generation.