Experimental measurement on pressure compressed single-walled and multi-walled carbon nanotube mats demonstrated low thermal conductivity of the mats which is bellow that exhibited by isotropic amorphous polymers. Using molecular dynamics simulations and theoretical analysis we propose that the very low thermal conductivity of carbon nanotube mats originates with low thermal conductance of contacts between carbon nanotubes which is due to very large mismatch between strong covalent bonds within the tubes and week Van der Waals bonding between the tubes. We discuss the possibility of good thermoelectric properties of carbon nanotube mats due to their low thermal conductivity

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