If the banjo became so hot you couldn't put your hand on it after a rebuild, my suspicion is the pre-loads on the carrier bearings and the pinion bearings were not set properly. In the case of the carrier bearings if they are too tight they can cause the bearing mount to spin on the carrier hubs instead of the roller elements rolling in the races. This is metal turning on metal and will certainly generate heat. In the case of the pinion bearings set too tight I have seen cases where the double race in the banjo spun. This will also generate heat.
Many on this forum have seen and used the differential rebuild dissertation posted on the web site of the Santa Anita A's of Arcadia, California.
www.santaanitaas.org Recently I did a rebuild for a club member and during the process I did a photo shoot of the entire process, which included having to remove the new carrier bearings to install shims. The photo shoot includes 65 photos with text.
This document has recently been posted on the web site right below the differential dissertation. Go to the home page of the web site and put your cursor on "Technical Reference", my name will appear below, click on it and it will bring up a menu of articles.
Scroll to "differential". The two articles are the differential rebuild, revised 2014, and right below, the photo shoot, 2015.
All are welcome to download and print these articles out.
Tom Endy