  We analyze reheating scenarios where a hidden sector is populated during
reheating along with the sector containing the Standard Model. We numerically
solve the Boltzmann equations describing perturbative reheating of the two
sectors, including the full dependence on quantum statistics, and study how
quantum statistical effects during reheating as well as the non-equilibrium
inflaton-mediated energy transfer between the two sectors affects the
temperature evolution of the two radiation baths. We obtain new power laws
describing the temperature evolution of fermions and bosons when quantum
statistics are important during reheating. We show that inflaton-mediated
scattering is generically most important at radiation temperatures $T\sim
M_\phi/4$, and build on this observation to obtain analytic estimates for the
temperature asymmetry produced by asymmetric reheating. We find that for
reheating temperatures $T_{\textrm{rh}} \ll M_{\phi}/4$, classical perturbative
reheating provides an excellent approximation to the final temperature
asymmetry, while for $T_{\textrm{rh}}\gg M_{\phi}/4$, inflaton-mediated
scattering dominates the population of the colder sector and thus the final
temperature asymmetry. We additionally present new techniques to calculate
energy transfer rates between two relativistic species at different
temperatures.
