In the present work, the thermal conductivity of three-dimensional metallic carbon nanostructure (T6) is investigated by employing the molecular dynamics (MD) simulations. In doing so, two different models of T6 nanostructure, i.e. beam- and plate-like, are chosen to study the effects of size and geometry on the thermal conductivity of the system. It is observed that length increase in beam-like T6 leads to a rise in the thermal conductivity. Also, higher cross-section area in equal length causes lower thermal conductivity. In the case of plate-like T6, the width increases of the structure results in a sharp reduction of the thermal conductivity. Furthermore, increasing the height of the structure in the same length and width causes a decrease in the thermal conductivity. Moreover, a beam-like T6 model is doped with different weight percentages of boron and nitrogen to study the effects of doping on the thermal conductivity. It is demonstrated that doping boron and nitrogen atoms in T6 nanostructure decreases the thermal conductivity drastically.