Thermal conductivity of a nickel-coated tri-wall carbon nanotube was studied using molecular dynamics where both the phonon and electron contributions were considered. Simulations predicted a significant effect of the metal coating on the thermal conductivity, i.e. 50% decrease for 1.2 nm of Ni coating. However, the decreasing rate of the thermal conductivity is minuscule for the metal thicker than 1.6 nm. The smaller thermal conductivity of the metal coating, phonon scattering at the interface, and less impacted heat transfer on the inner tubes of the carbon nanotube rationalized the observed trends.