The temperature dependent lattice thermal conductivity (κph) of MAX phases, Mn+1AXn are calculated using the Debye theory as outlined by Slack. At high temperature the formula derived by Slack is a reasonable approximation to estimate the lattice thermal conductivity. The calculation used the large data base of elastic coefficients of stable MAX phases established recently. It is found that MAX phases with “A”=Al have higher κph at 1300K, and the majority of MAX carbides have higher κph than MAX nitrides. We have also calculated the minimum thermal conductivities of these MAX phases using the empirical formula suggested by Clarke. It is shown that the minimal lattice thermal conductivities of MAX carbides and nitrides are closer to each other in the 211 phases than in higher n phases. The calculated κph for 8 MAX phases at 1300K are in reasonable agreement with experimental data, especially in Ti2AlC, Nb4AlC3, Ta4AlC3, Nb2AlC and Nb2SnC phases.