Rear end question

Well I finally got my Jeep mostly back together...well, far enough that I could test drive it Here's a little history: Over the winter, I completely rebuilt both axles. I swapped in some used 4.88's while I was in there. I just had it out for it's first drive. I live on a short private road so I could play with it a little bit. Anyway, I drove it back and forth for about 15-20 minutes at varying speeds. The fastest I could get it up to was maybe 40mph before I ran out of room and had to slow right down. There's a hill in the road so the gears had a chance to work both ways, under accel and decel. When I was done, I felt the housings. They both definately had some heat in them, not hot, but warm. Mostly right near the yoke or outer pinion bearing. They were making no noise whatsoever and got cooler as I got further away from the pinion. When I was setting the pinion bearing preloads I couldn't quite get them to the spec listed in my book so I erred on the loose side. There is still preload on the bearings though. They ended up being about 2-3 in/lbs looser than spec. Was I right to do this? So anyway, is this warmth normal? Should I worry about it? I'm assuming everything has to break in so I hope someone tells me I'm worrying about nothing!

 

No expert but yes it will build heat. How much I'm not sure.
No noise is good though.
I would check to make sure you have no movement of the pinion once a few more miles are on it.