The design of heat exchanger networks (HEN) in the process industry has largely focused on minimisation of operating and capital costs using techniques such as pinch analysis or mathematical modelling. Aspects of operability and flexibility, including issues of disturbances affecting downstream processes during the operation of highly integrated HEN, still need development. This work presents a methodology to manage temperature disturbances in a HEN design to achieve maximum heat recovery, considering the impact of supply temperature fluctuations on utility consumption, heat exchanger sizing, bypass placement and economic performance. Key observations have been made and new heuristics are proposed to guide heat exchanger sizing to consider disturbances and bypass placement for cases above and below the HEN pinch point. Application of the methodology on two case studies shows that the impact of supply temperature fluctuations on downstream heat exchangers can be reduced through instant propagation of the disturbances to heaters or coolers. Where possible, the disturbances have been capitalised upon for additional heat recovery using the pinch analysis plus-minus principle as a guide. Results of the case study show that the HEN with maximum HE area yields economic savings of up to 15% per year relative to the HEN with a nominal HE area.