Nickadamsaaa

Are they supposed to get warm after driving? My rear diff never warms up always room temp

when im going down the road if i give it gas it will make a humming noise and when letting off the gas it will make the humming noise had the front diff replaced 20k miles ago. scared its a bad diff or something major it doesnt do it when im in neutral if that helps. very puzzled

dont have pics yet but got a pretty good deal. looking for mods has intake and exhaust. have about 3000$ to spend thanks

not sure how to pm can someone help? interested