Following the nonequilibrium Green’s function formalism we study the thermal transport in a composite chain subject to a time-dependent perturbation. The system is formed by two finite linear asymmetric harmonic chains subject to an on-site potential connected together by a time-modulated coupling. The ends of the chains are coupled to two phononic reservoirs at different temperatures. We present the relevant equations used to calculate the heat current along each segment. We find that the system presents different transport regimes according the driving frequency and temperature gradients. One of the regimes corresponds to a heat pump against thermal gradient, thus a characterization of the cooling performance of the device is presented.