The ever-growing need to dissipate larger amounts of heat from components and structures requires the development of novel materials with superior thermal conductivity. Aligned carbon nanotube arrays that are integrated in composite materials and structures may prove useful in increasing heat transfer through their thickness. Theoretical studies have shown the potential of carbon nanotubes to reach a thermal conductivity of 6600 Wm(-1)K(-1). Experimental results on the arrays however have shown much lower thermal conductivity values. A study was conducted to better understand heat conduction in mm-long carbon nanotube arrays and to experimentally determine their thermal conductivity. Emphasis was placed on the effect of various parameters including the height and density of the array and the thermal resistance at the array interface. A method was devised to measure the thermal conductivity of the array relying on Fourier's law while maintaining a steady state one-dimensional heat flow. The study reveals that the taller the array and the higher its density, the larger the thermal conductivity of the array. Quantitative data is also provided on the effect of various interface materials and their deposition technique on the thermal conductivity of the arrays.