  We study thermal corrections to a model of real scalar dark matter
interacting feebly with a SM fermion and a gauge-charged vector-like fermion.
We employ the Closed-Time-Path (CTP) formalism for our calculation and go
beyond previous works by including the full dependence on the relevant mass
scales as opposed to using (non)relativistic approximations. In particular, we
use 1PI-resummed propagators without relying on the Hard-Thermal-Loop
approximation. We conduct our analysis at leading order in the loop expansion
of the 2PI effective action and compare our findings to commonly used
approximation schemes, including the aforementioned Hard-Thermal-Loop
approximation and results obtained from solving Boltzmann equations using
thermal masses as a regulator for $t$-channel divergences. We find that the
Boltzmann approach deviates between $-10\%$ and $+30\%$ from our calculation,
where the size and sign strongly depends on the mass splitting between the DM
candidate and the gauge-charged parent. The HTL-approximated result is more
precise for small gauge couplings and is percent level accurate for large mass
splittings, whereas it overestimates the relic density up to $25 \%$ for small
mass splittings. Tree-level propagators lead to underabundant DM as they do not
account for scattering contributions and can deviate up to $-100\%$ from the
1PI-resummed result.
