This is a common problem, but whilst I have not heard of an oil thermostat, almost certainly the replacement thermostat you have fitted is faulty. If it is an inline thermostat you fitted, it is either faulty, fitted incorrectly, or is letting too much coolant past before it opens.
The full definitive background is
HERE (a very long read)
How to fit the thermostat is
HERE from
THIS post.
My personal preference is a
Wahler 3029.89. If you could get a 3029.92 it would be better, but these are difficult to find, and expensive. But others are acceptable.
An alternative option is the
Meziere inline housing.
Load on the engine and distance is important, speeds of between 40-70mph for 10 miles should see it reach temperature of 82-88 degrees.
There is a lot of information about this issue and modification.
Search inline thermostat and you will see. If you decide to read it all, the winter will be over, and you will not notice lol.
If you really want to replace the oil cooler, Mickyboy has one listed
HERE. But I would still confirm the inline thermostats first.