  We investigate, by means of numerical lattice simulations, the
$\theta$-dependence of the critical deconfinement temperature of
$\mathrm{SU}(N)$ gauge theories at large $N$: $T_c(\theta) =
T_c(0)[1-R\theta^2+O(\theta^4)]$, with $R\sim O(1/N^2)$. We follow two
different strategies to determine $R$, one based on the calculation of the
latent heat of the transition and on the jump of the topological susceptibility
at the $\theta=0$ critical point, the other relying on a direct probe of
$T_c(\theta)$ by means of imaginary-$\theta$ Monte Carlo simulations. Our
results show that $R$ follows the expected large-$N$ scaling.
