  We investigate threshold resummation of soft gluon corrections for the
s-channel process of a single top quark production in association with a Higgs
boson in the Standard Model. We choose to work in the three-particle invariant
mass kinematics in direct QCD, i.e. in the space of Mellin moments. Our results
take into account terms of up to next-to-leading logarithmic (NLL) precision,
as well as $\mathcal{O} (\alpha_s)$ non-logarithmic terms which do not vanish
at threshold. After presenting analytical expressions we discuss the
corresponding numerical results for the total cross section and the invariant
mass distributions at the LHC.
