Hmmm. I'm only turning 35s though....
I assume you are running the stock steering pump? yes put in a cooler or bigger pump. The stock toyota pump was only built to handle a small 28in somthin tire, not 35s! thats a lot of tire to push. especially with a locker like you mentioned.
Defiantly install the cooler and let us know if you find a way to put in a jeep pump, I would really like to upgrade mine as well!