  We discuss the thermal evolution and Bose-Einstein condensation of
ultra-light dark matter particles at finite, realistic cosmological
temperatures. We find that if these particles decouple from regular matter
before Standard model particles annihilate, their temperature will be about 0.9
K. This temperature is substantially lower than the temperature of CMB
neutrinos and thus Big Bang Nucleosynthesis remains unaffected. In addition the
temperature is consistent with WMAP 7-year+BAO+H0 observations without
fine-tuning. We focus on particles of mass of $m\sim 10^{-23}$ eV, which have
Compton wavelengths of galactic scales. Agglomerations of these particles can
form stable halos and naturally prohibit small scale structure. They avoid
over-abundance of dwarf galaxies and may be favored by observations of dark
matter distributions. We present numerical as well as approximate analytical
solutions of the Friedmann-Klein-Gordon equations and study the cosmological
evolution of this scalar field dark matter from the early universe to the era
of matter domination. Today, the particles in the ground state mimic
presureless matter, while the excited state particles are radiation like.
