The Boltzmann entropy equation is commonly used in statistical interpretation of entropy to relate entropy $S$ with the number of microstates $\Omega$:
$$S=k\ln(\Omega) \, .$$
The classical thermodynamic entropy $S$ is related to heat $Q$ and absolute temperature $T$:
$$dS=\frac{\delta Q}{T} \, .$$
Now, the number of microstates $\Omega$ for the distribution of energy to the particles in a system happens to depend on temperature $T$, the partition function $P$, and the number of particles $n$ (assuming constant volume):
$$\ln(\Omega_{\mathrm{thermal}}) = n\ln(P) + \frac{U}{kT}$$
$$P=\sum{\exp \left( {-\frac{E_i}{kT}} \right)} \, .$$
So it seems that the dependence of $\Omega_{\mathrm{thermal}}$ on temperature in the above equation links the classical thermal entropy and the statistical thermal entropy.
However, I'm not aware of $\Omega_\text{config}$, the number of spatial configuration microstates, as having a similar dependence on temperature $T$ or internal energy $U$.
So why is the Boltzmann entropy equation is also used for the case of configuration entropy?
Doing so would seem to imply that there is heat transfer involved in changing the configuration entropy.