Given uncertainty in the processes involved in polar amplification, elucidating the role of poleward heat and moisture transport is crucial. To address this, I use the protocol of the Polar Amplification Modeling Intercomparison Project (PAMIP) to robustly separate the effects of sea ice loss from ocean surface warming under climate change. A moist isentropic circulation framework accounts for moisture transport, condensation and eddy transport, while connecting the mid-latitudes and the Arctic. It is found that sea ice loss reduces poleward heat transport by warming the returning branch of the moist isentropic circulation at high latitudes, while warming of the ocean surface strengthens the overturning circulation, increasing the net poleward heat transport.