A pulse combustion heat exchanger having a longitudinal axis is configured to accept oxidant and fuel and output a cooled combustion stream. The pulse combustion heat exchanger includes an oxidant inlet section that accepts oxidant, a fuel inlet section that accepts fuel, a mixing section that mixes oxidant with fuel, a combustion section that receives the oxidant and fuel and produces a pulsating combustion stream, and a heat transfer section configured to receive the pulsating combustion stream, the heat transfer section includes one or more resonance conduits. Coolant is employed at a plurality of longitudinally spaced-apart transition sections to remove heat.