  Spin polarization of neutron matter at finite temperatures and strong
magnetic fields up to $10^{18}$ G is studied in the model with the Skyrme
effective interaction. It is shown that, together with the thermodynamically
stable branch of solutions for the spin polarization parameter corresponding to
the case when the majority of neutron spins are oriented opposite to the
direction of the magnetic field (negative spin polarization), the
self-consistent equations, beginning from some threshold density, have also two
other branches of solutions corresponding to positive spin polarization. The
influence of finite temperatures on spin polarization remains moderate in the
Skyrme model up to temperatures relevant for protoneutron stars, and, in
particular, the scenario with the metastable state characterized by positive
spin polarization, considered at zero temperature in Phys. Rev. C {\bf 80},
065801 (2009), is preserved at finite temperatures as well. It is shown that
above certain density the entropy for various branches of spin polarization in
neutron matter with the Skyrme interaction in a strong magnetic field
demonstrates the unusual behavior being larger than that of the nonpolarized
state. By providing the corresponding low-temperature analysis, it is clarified
that this unexpected behavior should be addressed to the dependence of the
entropy of a spin polarized state on the effective masses of neutrons with spin
up and spin down, and to a certain constraint on them which is violated in the
respective density range.
