Embodiments include systems and methods for processing a feed gas and acid gas removal. A method may comprise receiving a feed gas to an absorber; contacting the feed gas counter-currently with a lean solvent stream to remove acid gas from the feed gas; producing a treated feed gas stream from the absorber; producing a rich solvent stream from the absorber comprising H2S and CO2 removed from the feed gas; receiving a side stream from the absorber to a side cooler; removing at least a portion of the heat of absorption from the side stream by the side cooler; producing a first output stream from the side cooler that is routed back into the absorber at a point below a draw point for the side stream; and producing a second output stream from the side cooler that is routed back into the absorber at a point below the first output stream.