The lattice specific heat in carbon nanotubes is evaluated within the microscopic model proposed by Mahan and Jeon, published in the Physical Review B, in 2004. Phonons are considered for single wall carbon nanotubes in armchair configuration. As expected, low temperature and high temperature regions show different behaviour of specific heat. Carbon nanotubes are also displaying a very interesting lattice transport depending on the tube diameter, with high thermal conductivities for small diameters.