The impact of decorated dislocations on the effective thermal conductivity of GaN is investigated by means of equilibrium molecular dynamics simulations via the Green-Kubo approach. The formation of "nanowires" by a few atoms of In in the core of dislocations in wurtzite GaN is found to affect the thermal properties of the material, as it leads to a significant decrease of the thermal conductivity, along with an enhancement of its anisotropic character. The thermal conductivity of In-decorated dislocations is compared to the ones of pristine GaN, InN, and random and ordered InxGa1-xN alloy, to examine the impact of doping. Results are explained by the stress maps, the bonding properties and the phonon density of states of the aforementioned systems. The decorated dislocations engineering is a novel way to tune, among other transport properties, the effective thermal conductivity of materials at the nanoscale, which can lead to the manufacturing of interesting candidates for thermoelectric or anisotropic thermal dissipation devices.