Rear end grinding

I have an 88 Jeep Wrangler that I have recently rebuilt the engine for and thought I was in the clear. I am now facing a rear end problem... If I run the jeep for more than 20 minutes, I am starting to hear a "grinding" noise from the rear end. The sound is very loud as if the rear end is going to fall apart. It only occurs when I am turning either direction uphill. Sometimes on flatland, also when I am turning in either direction. I think it has something to do with the rear end getting hot, because it doesn't do it in the morning or when I first start driving it. I am not even close to a mechanic, but I was hoping someone would see this and know where I should start as far as trouble shooting or fixing the problem. Thanks a million!

Its quite likely you have a limited slip differential. The noise is from the clutch packs slipping, as they are supposed to, when going around a corner.
Remove the cover, clean off the inside and the magent, (it should have one in the housing) and put in new gear lube, that is intended for positration differentials.
chances are the noise will go away.