Classical molecular dynamics (MD) simulations employing Brenner potential for intra-nanotube interactions and Van der Waals forces for polymer-nanotube interfaces are used to invetigate the thermal expansion and diffusion characteristics of carbon nanotube-polyethylene composites. Additions of carbon nanotubes to polymer matrix are found to increase the glass transition temperature Tg, and thermal expansion and diffusion coefficients in the composite above Tg. These findings could have implications in CNT composite processing, coating and painting applications.