  We investigate theoretically magnetoentropic signatures of the crystal phase
of magnetic skyrmions of various kinds, commonly appearing in two dimensions,
\textit{viz.}, N\'eel, Bloch and anti skyrmions. Using Monte Carlo calculations
based on spin Hamiltonians, we obtain magnetic entropy change $\Delta S_m$ in
the presence of three different types of Dzyaloshinskii-Moriya interactions
responsible for these skyrmions. The phase mapping of $\Delta S_m$ using
skyrmion counting number $N_{sk}$ in temperature-magnetic field plane reveals
fluctuation-dominated weak first-order transition in the precursor phase of the
skyrmions, and a sign change in $\Delta S_m$ when the system enters into the
skyrmion crystal phase -- in agreement with recent experimental findings. We
also find that the fractional entropy change in going from a ferromagnetic
phase to the skyrmion crystal phase is much larger compared to the conventional
route of paramagnetic phase to ferromagnetic phase, used for the purpose of
magnetic cooling. The magnetoentropic signatures of the different types of
skyrmion crystals are found to be similar. Our results indicate that the
skyrmion crystals exhibit enhanced cooling efficiency and have the potential to
upgrade the existing magnetic cooling methods.
