  We consider QCD radiative corrections to the production of a heavy-quark pair
in hadronic collisions. We present the computation of the soft-parton
contributions at low transverse momentum of the heavy-quark pair up to second
order in the QCD coupling $\alpha_s$. These results complete the evaluation at
the next-to-next-to-leading order (NNLO) of the transverse-momentum resummation
formula for this process. Moreover, they give all the ingredients that are
needed for the NNLO implementation of the qT subtraction formalism for
heavy-quark production. We discuss the details of the computation and we
provide a code that can be used to obtain the relevant results in numerical
form.
