Does an external transmission cooler on a auto help the coolant temp to reduce as the radiator will have less stress to cool the transmission as well?

my car usually goes up to 105 Celsius or 221 Fahrenheit usually after 3 or 4 runs but stays to 98 Celsius on normal drive with A/C on ..new nismo thermostat new radiator and coolant 50/50 installed bleed the system 3 times.

will an external transmission cooler help??

 

I don't think it could hurt, just make sure you account for the additional fluid needed.