Owing to recent observations of superconductivity in quasi-one-dimensional (1D) systems, Josephson arrays composed of aligned and weakly coupled 1D superconducting nanowires have attracted renewed interest for modeling the experimental data. Carrying out Monte Carlo simulations, we go beyond the traditional mean field results to show that the competition between 1D fluctuations and the transverse Josephson coupling between the nanowires can lead to a 1D–3D crossover transition at a temperature Tc below the mean field TCO of the wires, with interesting and surprising pre-transitional characteristics. In particular, the specific heat exhibits a rounded peak between Tc and TCO, and the phase correlation length within the transverse ab plane diverges at Tc from above, in a manner consistent with that of a 2D Berezinskii–Kosterlitz–Thouless transition. Simultaneous with the above, quenching of phase fluctuations along the c-axis of the wires is also seen to occur at Tc. These behaviors are in excellent agreement with the experimental manifestations observed in the superconductivity of 4 Å carbon nanotubes.