  We investigate the heat conduction in a quasi 1-D gas model with various
degree of chaos. Our calculations indicate that the heat conductivity $\kappa$
is independent of system size when the chaos of the channel is strong enough.
The different diffusion behaviors for the cases of chaotic and non-chaotic
channels are also studied. The numerical results of divergent exponent $\alpha$
of heat conduction and diffusion exponent $\beta$ are in consistent with the
formula $\alpha=2-2/\beta$. We explore the temperature profiles numerically and
analytically, which show that the temperature jump is primarily attributed to
superdiffusion for both non-chaotic and chaotic cases, and for the latter case
of superdiffusion the finite-size affects the value of $\beta$ remarkably.
