  The specific heat of the superconducting cuprates is calculated over the
entire phase diagram. A d-wave BCS approach based on the large Fermi surface of
Fermi liquid and band structure theory provides a good description of the
overdoped region. At underdoping it is essential to include the emergence of a
second energy scale, the pseudogap and its associated Gutzwiller factor, which
accounts for a reduction in the coherent piece of the electronic Green's
function due to increased correlations as the Mott insulating state is
approached. In agreement with experiment, we find that the slope of the linear
in T dependence of the low temperature specific heat rapidly increases above
optimum doping while it is nearly constant below optimum. Our theoretical
calculations also agree with recent data on Bi$_2$Sr$_{2-\rm x}$La$_{\rm
x}$CuO$_{6+\delta}$ for which the normal state is accessed through the
application of a large magnetic field. A quantum critical point is located at a
doping slightly below optimum.
