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Following our recent study on the electronic properties of rough nanoribbons , in this paper the role of geometrical and roughness parameters on the thermal properties of armchair graphene nanoribbons is studied. Employing a fourth nearest-neighbor force constant model in conjuction with the nonequilibrium Green's function method the effect of line-edge-roughness on the lattice thermal conductivity of rough nanoribbons is investigated. The results show that a reduction of about three orders of magnitude of the thermal conductivity can occur for ribbons narrower than 10 nm. The results indicate that the diffusive thermal conductivity and the effective mean free path are directly proportional to the ribbon's width and the roughness correlation length, but inversely proportional to the roughness amplitude. Based on the numerical results an analytical model for the thermal conductivity of narrow armchair graphene nanoribbons is proposed in this paper. The developed model can be used in the analysis of graphene-based nano transistors and thermoelectric devices, where the appropriate selection of geometrical and roughness parameters are essential for optimizing the thermal properties.