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.
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