The molecular dynamics simulation with the use of the empirical Tersoff potential is applied to study the thermal characteristics of carbon nanotubes (CNTs). A thermal reservoir is devised to control the temperature and to exact the heat flux input. The quantum effect defining the precise temperature from the absolute zero Kelvin and up is included by applying phonon (boson) statistics to the specific heat. At low temperature, the CNT thermal conductivity increases with increasing temperature. After reaching its peak, which is limited by the length of the CNT, it decreases with temperature due to phonon-phonon interactions. The scaling law of thermal conductivity as a function of temperature and length is inferred from the simulation results, allowing prediction for CNTs of much longer length beyond what MD could simulate.