The molecular dynamics (MD) simulation was used to investigate the effect of nanotube diameter on heat pulse propagation in thin armchair single walled carbon nanotubes. A picosecond heat pulse was applied in the middle of each nanotube. The heat pulse generated several wave packets, which gradually leave diffusive background and propagate along the nanotube with the speed of sound waves. These wave packets correspond to the second sound waves and twisting (TW) phonon mode. It was found that by increasing the nanotube diameter the contribution of second sound waves to heat transportation decreases while the contribution of TW phonon mode increases. Also, it was observed that the propagation speeds of wave packets increase with increasing nanotube diameter. This observation was explained by taking into account the effect of nanotube diameter on C–C bond lengths and eventually on the modulus of elasticity of armchair SWCNTs.