  We study the non-equilibrium dynamics of a pseudoscalar axion-like particle
(ALP) weakly coupled to degrees of freedom in thermal equilibrium by obtaining
its reduced density matrix. Its time evolution is determined by the in-in
effective action which we obtain to leading order in the (ALP) coupling but to
\emph{all orders} in the couplings of the bath to other fields within or beyond
the standard model. The effective equation of motion for the (ALP) is a
Langevin equation with noise and friction kernels obeying the fluctuation
dissipation relation. A ``misaligned'' initial condition yields damped coherent
oscillations, however, the (ALP) population increases towards thermalization
with the bath. As a result, the energy density features a mixture of a cold
component from misalignment and a hot component from thermalization with
proportions that vary in time $(cold)\,e^{-\Gamma t}+(hot)\,(1-e^{-\Gamma t})$,
providing a scenario wherein the ``warmth'' of the dark matter evolves in time
from colder to hotter. As a specific example we consider the (ALP)-photon
coupling $g a \vec{E}\cdot \vec{B}$ to lowest order, valid from recombination
onwards. For $T \gg m_a$ the long-wavelength relaxation rate is substantially
enhanced $\Gamma_T = \frac{g^2\,m^2_a\,T}{16\pi} $. The ultraviolet divergences
of the (ALP) self-energy require higher order derivative terms in the effective
action. We find that at high temperature, the finite temperature effective mass
of the (ALP) is $m^2_a(T) = m^2_a(0)\Big[ 1-(T/T_c)^4\Big]$, with $T_c \propto
\sqrt{m_a(0)/g}$, \emph{suggesting} the possibility of an inverted phase
transition, which when combined with higher derivatives may possibly indicate
exotic new phases. We discuss possible cosmological consequences on structure
formation, the effective number of relativistic species and birefringence of
the cosmic microwave background.
