In a previous publication, we have presented a model for the photoproduction of $mathrm{J/}psi$ vector mesons off protons, where the proton structure in the impact-parameter plane is described by an energy-dependent hot-spot profile. Here we extend this model to study the photonuclear production of $mathrm{J/}psi$ vector mesons in coherent and incoherent interactions of heavy nuclei. We study two methods to extend the model to the nuclear case: using the standard Glauber-Gribov formalism and using geometric scaling to obtain the nuclear saturation scale. We find that the incoherent cross section changes sizably with the inclusion of subnucleonic hot spots, and that this change is energy dependent. We propose to search for this behavior by measuring the ratio of the incoherent to coherent cross section at different energies. We compare the results of our model to results from RHIC and from the Run 1 at the LHC finding a satisfactory agreement. We also present predictions for the LHC at the new energies reached in Run 2. The predictions include $mathrm{J/}psi$ production in ultra-peripheral collisions, as well as the recently observed photonuclear production in peripheral collisions.
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