6.0 power steering pump question

[ALLJ]

I have a 03 LS 6.0 in my 06 jeep TJ with a 79 Ford HP D60 in the front with a Detroit and lockouts when its in 4WD after a few minutes of driving the pump stars whinning like its low of fluid I have narrowed the problem down to the fluid getting hot I can let it set for 15-20 minutes and its fine till you crawl around for a few minutes and it starts again It drives fine on the road with no issues just when Im off road in 4WD Lo range
The question I have has any of you had this problem with the stock pump ? would a steering cooler fix it ? do I need hydro assist and a cooler ? any information will be appreciated

 

[Last Rebel]

we put a 6.0 in a yj. we didn't have any issues with the pump in it's stock form and it has been steering 39 inch pit bulls since it was built. he didn't have the money to install hydraulic assist during the build, so we ran without it for awhile. no issues. we installed a PSC ram assist and they recommend running a cooler with at least 4 passes. putting a cooler with at least this many passes in front of your radiator should help it with or without the the ram assist kit, but the ram assist is a major plus with large tires. i also have it on my cj with 38 inch tires and i'm planning on going to 39s when these are worn down a little more. i hope this helps you out.

 

[ALLJ]

Thanks Im running 37s on it now Im thinking about trying the cooler just to see what happens I know there are alot of these motors out there in buggys and jeeps running alot bigger tires than I am and I was thinking that surely I was not the only one that has ever had this issue