  We present a detailed investigation of the impact of astrophysical processes
on the shape and amplitude of the kinetic Sunyaev-Zel'dovich (kSZ) power
spectrum from the post-reionization epoch. This is achieved by constructing a
new model of the kSZ power spectrum which we calibrate to the results of
hydrodynamic simulations. By construction, our method accounts for all relevant
density and velocity modes and so is unaffected by the limited box size of our
simulations. We find that radiative cooling and star-formation can reduce the
amplitude of the kSZ power spectrum by up to 33%, or 1 uK^2 at ell = 3000. This
is driven by a decrease in the mean gas density in groups and clusters due to
the conversion of gas into stars. Variations in the redshifts at which helium
reionization occurs can effect the amplitude by a similar fraction, while
current constraints on cosmological parameters (namely sigma_8) translate to a
further +-15% uncertainty on the kSZ power spectrum. We demonstrate how the
models presented in this work can be constrained -- reducing the astrophysical
uncertainty on the kSZ signal -- by measuring the redshift dependence of the
signal via kSZ tomography. Finally, we discuss how the results of this work can
help constrain the duration of reionization via measurements of the kinetic SZ
signal sourced by inhomogeneous (or patchy) reionization.
