The process of manufacturing an oil cooler which comprises the steps of:(A) making cooling fins by forming a plurality of insertion holes of which inner brim is projected along the axial direction for inserting a plurality of tubes in each sheet to be transformed into cooling fins, and to drill a plurality of pores for inserting linear brazing materials at positions closed to the insertion holes, respectively,(B) inserting a plurality of tubes arranged in parallel into each of insertion holes of a number of the cooling fins respectively, and inserting linear brazing materials into the pores of each of the cooling fins, and(C) joining the brims of the cooling fins and the tubes by heating to melt said brazing materials.