hi
The internal cooler in the radiator is not big enough , it brings the trans oil upto operating temp then keeps it there. It will never transmit enough heat to cause overheating of the engine even thou its a very efficient fluid to fluid type . Its to small .
Many makers when towbar was specified offered an additional cooler . IT was run in series with the rad internal cooler. The factory add on coolers were mostly to small also .

It does not help when using a factory style in rad cooler that engines must be run at 100-105 cel . The trans will then have no choice but to run at a high level also .

hi
Operating temp of engine is +/- 95 deg cel so this only gives u 5 deg to play with . From experience u will get that rise from a loaded 8x 5 trailer .
Fit for purpose NOT.

Synthetic engine oils definition has been watered down . If its 100% manmade its synthetic not the imposters /fake wanna bees . Try both types there is a big difference . The difference was argued in court Mobil vs Castrol . Unfortunately Castrol won . This was not a benefit to consumers it was to benefit Castrol`s bank balance . The customer lost that day .

Engineered oil will last way longer than mineral easily . But in a racing environment is still contaminated easily . The excessive heat also degrades just not as fast as mineral . Oil still needs to be changed regularly .

A radiator in a passenger car will not overheat with cooler in front of it .