Symmetry of the energy gap and specific heat in BCS theory

I know that in BCS theory an energy gap $Delta(mathbf{k})$ with s-wave symmetry would lead, in the limit for very low temperature, to a term in the free energy proportional to:

$$
F simeq e^{-beta Delta_0}
$$

where $Delta_0$ is zero-temperature value of the s-wave energy gap, and $beta = k_B T $. By derivation, one obtains therefore for the specific heat the very same behaviour. As for my understanding, this is due to the fully gapped spectrum of the elementary excitation, where the energy dispersion is now

$$
E_k = sqrt{( xi^2_k + Delta^2_k )}
$$

$xi_k$ being the normal dispersion relation with respect to the chemical potential.

Now, what happens for an energy gap with d-wave symmetry? In principle the energy spectrum of the excitation is not fully gapped, as we have nodal points in k-space, and we can also linearise the spectrum around these points. Would the free energy and the specific heat be different in this case (e.g. showing a power law)? Are there analytical or numerical result?

Can we then claim there is an effect of the symmetry of the energy gap in the specific heat? Considering the real energy gaps are so small (order of meV) that one might need to reach extremely low temperatures to find the exponential behaviour, could this difference be experimentally measured?

Any help in this topic will be highly appreciated!
Thanks!:)