Yep, the oil cooler will allow engine oil to enter the cooling system, here is a guide to help you see what's going on and I have included the oil cooler replacement instructions as well.
https://www.2carpros.com/articles/engine-oil-inside-the-radiator
There is also an engine cooler system thermostat which I would change if there were sludge inside the engine, please change the oil and filter once the job is completed as well. Check out the images (below). Let us know if you need anything else.
Images (Click to make bigger)
Tuesday, February 18th, 2025 AT 10:37 AM