  Model-independent theoretical upper bound on the thermal dark matter (DM)
mass can be derived from the maximum inelastic DM cross-section featuring the
whole observed DM abundance. We deploy partial-wave unitarity of the scattering
matrix to derive the maximal thermally-averaged cross section for general
number-changing processes $r\to 2$ (with $r\ge 2$), which may involve standard
model particles or occur solely within the dark sector. The usual upper limit
on the DM mass for $s$-wave annihilation is around 130 TeV (1 GeV) for $r=2$
(3), only applies in the case of a freeze-out occurring in the standard
cosmological scenario. We consider the effects of two nonstandard cosmological
evolutions, characterized by low-temperature reheating: $i)$ a kination-like
scenario and $ii)$ an early matter-dominated scenario. In the first case, early
freeze-out strengthens the unitarity bound to a few TeVs for WIMPs; while in
the second case, the WIMP DM can be as heavy as $\sim 10^{10}$ GeV due to a
large entropy dilution.
