We investigate the large-N behavior of the topological susceptibility X in four-dimensional SU(N) gauge theories at finite temperature, and in particular across the finite-temperature transition at T-c. For this purpose, we consider the lattice formulation of the SU(N) gauge theories and perform Monte Carlo simulations for N = 4,6. The results indicate that X has a nonvanishing large-N limit for T < T-c, as at T = 0, and that the topological properties remain substantially unchanged in the low-temperature phase. On the other hand, above the deconfinement phase transition, X shows a large suppression. The comparison between the data for N = 4 and N = 6 hints at a vanishing large-N limit for T > T-c.
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