  We study the effects of finite stellar temperatures on the oscillations of
superfluid neutron stars. The importance of these effects is illustrated with a
simple example of a radially pulsating general relativistic star. Two main
effects are taken into account: (i) temperature dependence of the entrainment
matrix and (ii) the variation of the size of superfluid region with
temperature. Four models are considered, which include either one or both of
these two effects. Pulsation spectra are calculated for these models, and
asymptotes for eigenfrequencies at temperatures close to critical temperature
of neutron superfluidity, are derived. It is demonstrated that models that
allow for the temperature effect (ii) but disregard the effect (i), yield
unrealistic results. Eigenfunctions for the normal- and superfluid-type
pulsations are analyzed. It is shown that superfluid pulsation modes
practically do not appear at the neutron-star surface and, therefore, can
hardly be observed by measuring the modulation of the electromagnetic radiation
from the star. The e-folding times for damping of pulsations due to the shear
viscosity and nonequilibrium modified Urca processes are calculated and their
asymptotes at temperatures close to the neutron critical temperature, are
obtained. It is demonstrated that superfluid pulsation modes are damped by 1--3
orders of magnitude faster than normal modes.
