= Solution
{c}
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> $\rho cT\,dV$, measured relative to the reference at which $T=0$. Summing over $\Omega$ gives
$$
\boxed{E_\Omega(t)=\iiint_\Omega\rho cT(\mathbf x,t)\,dV.}
$$
Choosing 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>.
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