Two key simplifying assumptions, made in Part I of this work, are that the heat exchange times are negligible compared with the batch processing time and that matches occur between batches of material as they are transferred from unit to unit. The latter assumption results in countercurrent heat exchanges. In this paper, these assumptions are relaxed and an extension to the formulation developed which accommodates finite exchange times as well as heat exchange with batches during their processing. The extended formulation thus addressed multiple heat exchange modes : countercurrent, cocurrent, and combinations of the two. The basic mixed integer linear programming formulation is further augmented to accommodate heat integration across independent cyclically operated batch production lines. A solution approach to the resulting large scale MILP formulation is developed based on Benders’ decomposition and is demonstrated with a two production line example. Finally, the issue of sharing of heat exchange units across multiple matches and the related design problem of minimizing the number of multipurpose heat exchange units are discussed. The sharing feature is shown to lead to complex mixed integer nonlinear constraints.