Abstract : We discuss the transport properties of a class of Hamiltonian dynamics with local confinement, in which interactions between neighboring particles occur through hard core elastic collisions. Such dynamics may be described as high-dimensional billiards. We consider the case where the collisions are rare and, for large systems, derive a Boltzmann-like equation for the evolution of the probability densities. We solve this equation in the linear regime and compute the heat conductivity in the approximate stationary state and with the help of the Green-Kubo formula. We demonstrate the validity of the molecular chaos hypothesis by comparing our theoretical predictions to the results of numerical simulations performed on a new class of models, which are defocusing chaotic billiards, likened to higher-dimensional stadia.