For the mixing of two streams having substantially different temperatures, a primary object of the present invention is to obtain significantly improved recovery of heating and/or refrigeration values by indirect heat transfer combined with staged heat and mass transfer. The process of the present invention is a fundamental departure from all previous processes of the prior art.An object of the present invention is to accomplish reverse or "inverse" distillation. While traditional distillation or staged absorption performs simultaneous heat and mass transfer to achieve a separation, the present invention uses that process to mix two feed streams to form a single mixed product stream.