  We study the resummation of the $0$-jettiness resolution variable
$\mathcal{T}_0$ for the top-quark pair production process in hadronic
collisions. Starting from an effective theory framework we derive a
factorisation formula for this observable which allows its resummation at any
logarithmic order in the $\mathcal{T}_0\to 0$ limit. We then calculate the
$\mathcal{O}(\alpha_s)$ corrections to the soft function matrices and, by
employing renormalisation group equation methods, we obtain the ingredients for
the resummation formula up to next-to-next-to-leading logarithmic
($\mathrm{NNLL}$) accuracy. We study the impact of these corrections to the
$0$-jettiness distribution by comparing predictions at different accuracy
orders: $\mathrm{NLL}$, $\mathrm{NLL}^\prime$, $\mathrm{NNLL}$ and approximate
$\mathrm{NNLL}^\prime$ ($\mathrm{NNLL}^\prime_{\text{a}}$). We match these
results to the corresponding fixed order calculations both at leading order and
next-to-leading order for the $t\bar{t}+$jet production process, obtaining the
most accurate prediction of the $0$-jettiness distribution for the top-quark
pair production process at $\mathrm{NNLL}^\prime_{\text{a}}+\mathrm{NLO}$
accuracy.
