We investigate the propagation of temperature perturbations in an array of coupled nonlinear oscillators at finite temperature. We evaluate the response function at equilibrium and show how the memory effects affect the diffusion properties. A comparison with nonequilibrium simulations reveals that the telegraph equation provides a reliable interpretative paradigm for describing quantitatively the propagation of a heat pulse at the macroscopic level. The results could be of help in understanding and modeling energy transport in individual nanotubes.