Has towing package ever proved inadequate?

I have 2014 sr5 v6 manual...does the pink fan clutch indicate I have the transmission cooler? Im really clueless when it comes to anything under the hood!

 

I don't tow anything near the tow rating but I do have heavy tires, a supercharger, and a lot of extra weight in armor on the truck. a 4000lb trailer was fine through windy mountain passes while the truck was also loaded down with all the expo/camping gear. I don't monitor trans temps but no temp light, no failure, and not much struggle doing 60mph uphill

 

No.
Transmission coolers are used on automatic transmissions, autos are fluid drive. The fluid heats and gets burned during heavy usage like towing. A cooler helps.

 

That was the beer typing. TOW

 

Thanks for the response, pardon my ignorance when it comes to that. Curious...why out of all parts is that the pink?

 

I have a 6 speed but pulled 9000lb and had no problems.