  We study the post-inflationary dynamics for reheating and freeze-in dark
matter in the Higgs-$R^2$ inflation model. Taking the perturbative approach for
reheating, we determine the evolution of the temperature for radiation bath
produced during reheating and determine the maximum and reheating temperatures
of the Universe. Adopting a singlet scalar dark matter with a conformal
non-minimal coupling and a vanishing Higgs-portal coupling, we discuss the
freeze-in production of dark matter both from the non-thermal scattering during
reheating and the thermal scattering after reheating. We find that thermal
scattering is dominant for dark matter production in our model due to the high
reheating temperature. The reheating temperature in our model is determined
dominantly by the Higgs condensate to be up to about $10^{14}\,{\rm GeV}$ and
dark matter with masses up to about $10^9\,{\rm GeV}$ can be produced with a
correct relic density.
