There are two opposing effects at work here - radial thickness and surface area, neither of them probably very significant. The additional thickness of the paint layer adds thermal insulation between the conductor and air; I don't have data but would not be surprised if the thermal resistance of the paint is relatively similar to the sheath material. Since it is applied as a liquid there should not be any significant voids between sheath and paint to create an extra boundary layer.
But the addition of the paint also increases the overall diameter and hence the surface area, the latter more so if the paint surface is less smooth than the sheath. Since a significant part of the thermal resistance from conductor to ambient comes from the interface to the air, it is quite possible that the two effects cancel partially or completely, or even that the additional surface area improves the heat dissipation.