  We propose a model with a quantized degree of freedom to study the heat
transport in quasi-one dimensional system. Our simulations reveal three
distinct temperature regimes. In particular, the intermediate regime is
characterized by heat conductivity with a temperature exponent $\gamma$ much
greater than 1/2 that was generally found in systems with point-like particles.
A dynamical investigation indicates the occurrence of non-equipartition
behavior in this regime. Moreover, the corresponding Poincar\'e section also
shows remarkably characteristic patterns, completely different from the cases
of point-like particles.
