  In this paper, we prove that the group $\mathrm{Aut}_\mathbb{Q}(X)$ of
numerically trivial automorphisms are uniformly bounded for smooth projective
threefolds $X$ of general type which either satisfy $q(X)\geq 3$ or have a
Gorenstein minimal model. If $X$ is furthermore of maximal Albanese dimension,
then $|\mathrm{Aut}_\mathbb{Q}(X)|\leq 4$, and equality can be achieved by an
unbounded family of threefolds previously constructed by the third author.
Along the way we prove a Noether type inequality for log canonical pairs of
general type with the coefficients of the boundary divisor from a given subset
$\mathcal{C}\subset (0,1]$ such that $\mathcal{C}\cup\{1\}$ attains the
minimum.
