An apparatus and method for cooling hot fluids, especially exhaust gases, with a multi-pass cooler core. The cooler core is particularly useful for cooling exhaust gases flowing in an exhaust gas recirculation (EGR) system or regime in operative association with an internal combustion engine, such as a diesel engine. Cooled gases are recirculated to the engine input to help reduce noxious exhaust emissions. The invention utilizes unequal areas-in-flow between the first exhaust pass through the core and the second and subsequent passes through the core. The first pass through the core features an area-in-flow comparatively larger than the area-in-flow of the second pass. The difference in areas-in-flow between passes influences gas velocities to reduce fouling, despite changes in exhaust gas temperature between passes through the core.