If the engine seized, there will be a lot of internal damage, the oil cooler cannot be reused, there is a good chance that there are still metal residues in the oil cooler.
If you do so anyway, there is a good chance that remaining metal particles will cause significant damage to the engine and you will have to start from scratch. This would be disproportionate to the cost of a new oil cooler. Also a used or overhauled oil cooler is strongly discouraged, you usually do not know the history of this part, the risk you run is much too high.
In air-cooled engines, the oil cooler is one of the most important parts, it ensures the cooling of the engine. With a water-cooled engine, it's a little different, there the oil cooler is used as a heat exchanger and only with some 2100 cc Waterboxers and all diesel engines.
Instructions
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