The growth of single wall carbon nanotubes (SWNTs) mediated by metal nanoparticles is considered within (i) the surface diffusion growth kinetics model coupled with (ii) a thermal model taking into account heat release of carbon adsorption-desorption on nanotube surface and carbon incorporation into the nanotube wall and (iii) carbon nanotube-inert gas collisional heat exchange. Numerical simulations performed together with analytical estimates reveal various temperature regimes occurring during SWNT growth. During the initial stage, which is characterized by SWNT lengths that are shorter than the surface diffusion length of carbon atoms adsorbed on the SWNT wall, the SWNT temperature remains constant and is significantly higher than that of the ambient gas. After this stage the SWNT temperature decreases towards that of gas and becomes nonuniformly distributed over the length of the SWNT. The rate of SWNT cooling depends on the SWNT-gas collisional energy transfer that, from molecular dynamics simulations, is seen to be efficient only in the SWNT radial direction. The decreasing SWNT temperature may lead to solidification of the catalytic metal nanoparticle terminating SWNT growth or triggering nucleation of a new carbon layer and growth of multiwall carbon nanotubes. (C) 2004 American Institute of Physics.