The paper considers a heat integration problem in a system of hot/cold batch vessels available in a given time interval, H, repeated several times in the planning period. The aim of the study is to propose a design procedure which exploits the system heat integration potential and ensures the desired vessel final temperatures at minimum total cost. It is assumed that matching between different pairs of hot/cold vessels is carried out in sequential subintervals within H including heating and cooling supplied by external utilities. In order to characterise the heat exchange equipment required for a given system, a generalised engineering parameter called conditionally Power of the Heat Exchanger (PHE) representing the basic heat exchange impact parameters, is introduced. The heat exchanger network design problem is formulated as a mixed integer non-linear programming (MINP) task under constraints of heat integration feasibility, order and duration of matching, installed PHE, external utility requirement and required temperatures. The approach is illustrated by an example.