Interplant heat integration (IPHI) using intermediate fluid circles provides an additional opportunity for energy saving and emission reduction, beyond traditional intraplant heat integration. However, the number of intermediate fluid circles as well as their heat capacity and temperatures are all variables. It is difficult to find promising solutions, since such conditions generally lead to nonlinearity. To deal with this problem, a transshipment type model, which holistically optimizes the parameters and interconnectivity patterns of intermediate fluid circles and keeps the constraints linear, is developed. New formulations are developed to identify exact distributions of intermediate fluid circles (namely heat transfer available intervals) among all temperature intervals, with unknown temperatures. Additionally, mixed-integer linear constraints are developed to describe interconnectivity patterns of intermediate fluid circles so as to calculate piping and pumping cost. The performances of different interconnectivity patterns are explored, while not only the energy efficiency but also the total cost are optimized. Case studies show that better results with lower TAC and appropriate interconnectivity patterns of intermediate fluid circles can be obtained, compared to the literature.