Results of extensive and accurate numerical studies on heat transfer in a system of particles with unequal masses, interacting through hard-point potentials with two types of symmetry, are reported. The particles are confined in a one-dimensional box with fixed ends coupled to heat reservoirs at different temperatures. The study aims to throw light upon recent controversial results on thermal conductivity in one-dimensional systems. When the particles interact through elastic hard-point collisions (a standard asymmetric case), the system is shown to have always infinite (anomalous) thermal conductivity as follows from the Prosen-Campbell theorem.