  Once the temperature of a bosonic gas is smaller than the critical, density
dependent, transition temperature, a Bose - Einstein Condensation process can
take place during the cosmological evolution of the Universe. Bose - Einstein
Condensates are very strong candidates for dark matter, since they can solve
some major issues in observational astrophysics, like, for example, the
galactic core/cusp problem. The presence of the dark matter condensates also
drastically affects the cosmic history of the Universe. In the present paper we
analyze the effects of the finite dark matter temperature on the cosmological
evolution of the Bose-Einstein Condensate dark matter systems. We formulate the
basic equations describing the finite temperature condensate, representing a
generalized Gross-Pitaevskii equation that takes into account the presence of
the thermal cloud in thermodynamic equilibrium with the condensate. The
temperature dependent equations of state of the thermal cloud and of the
condensate are explicitly obtained in an analytical form. By assuming a flat
Friedmann-Robertson-Walker (FRW) geometry, the cosmological evolution of the
finite temperature dark matter filled Universe is considered in detail in the
framework of a two interacting fluid dark matter model, describing the
transition from the initial thermal cloud to the low temperature condensate
state. The dynamics of the cosmological parameters during the finite
temperature dominated phase of the dark matter evolution are investigated in
detail, and it is shown that the presence of the thermal excitations leads to
an overall increase in the expansion rate of the Universe.
