Setting heat pumps correctly in a chemical process system can enhance the energy utilization ratio of the system, reduce the consumption of both the hot and cold utilities, and achieve utility savings and economic benefits. In this paper, for the case of introducing a single heat pump into a system, the dynamic changes of the grand composite curve and pinch temperature under different scenarios are analyzed using a graphical analysis method. The reasons and conditions for such changes are determined. It is shown that for cases that exhibit a change in pinch temperature more hot and cold utility savings may be obtained by using two heat pumps. Existing as well as new two-heat-pump arrangements that comply with the cross-pinch rule are presented.