Aftermarket Engine oil cooler make temp difference?

I have a 2016 Tacoma no tow package and have installed OEM hitch, a engine oil cooler, and getting ready to install transmission oil cooler after fluid change to start towing my car to track
After installation of engine oil cooler I drove street and highway to see if it would make a difference and the temps still pretty much follow the coolant temps these 2016 Tacoma's (no tow package) don't have the OEM heat exchangers so did I waste my time relocating filter and adding cooler to my Tacoma or with load of my car it would likely make a difference if anyone else done the same?

 

Pin the transmission open you should see an immediate difference (Like 10 - 30 deg F cooler).

 

I'm talking about the engine oil actually haven't installed the trans cooler yet

 

Engine oil temp is calculated by the ECU, there no actual sensor... adding the stock cooler will surely have the benefit of dropping engine oil temps some.

 

This was a after market engine oil cooler?

Did you install a oil temperature gauge?

Is the cooler controlled via thermostat? The down side without a thermostat is in real cold weather the oil takes longer to get up to temperature

I can see a big difference in oil temperature but my Tow vehicle is a 7.3 Ford.