While the basic principles of thermodynamics have remained the same, the necessity for heat exchangers to have good effectiveness in a small volume is constantly growing. Heat exchangers type Matrix Heat Exchanger (MHE), which can meet these requirements, does not have an optimal design variant for its use. These heat exchangers have been approached for 60 years, by many researchers, currently offering only an overview of the process. The mechanism of heat transfer in a matrix heat exchanger is complex, having three different thermal convection paths as well as thermal conduction through two different surfaces. This paper presents the simulations performed in ANSYS Workbench, combining all these heat transfer modes, for developing an optimal model of a perforated plate matrix heat exchanger, used for the pre-cooling of a hydrogen isotopes stream mixture, for purification purposes, as well as, for preparing the inlet temperature in cryogenic distillation columns of hydrogen isotopes.