Oh, my research was done, but I was busy, I can send you the book if you want, my curiosity has faded. Anyway long story short is he is not descendant directly fro Chingiz Khan his "hero" so to speak, he is descendant from what it seems like a Mongolian Family that have been Turkicized. "Temür’s marriage to a Chinggisid princess (the daughter of Qazan Khan) gave him the right to use the title kürgän, or imperial son in law, which was also adopted by several of his descendants, and he attempted to revive the Chinggisid house through the elevation of puppet khans in the Ulus Chaghadai" my source is the new Cambridge History of Islam. I can send it to you if you like, on the Mughals part they see themselves as Timurids, but the correct word is Gurkani, a simple google book search has concluded me that Babur's diary called Baburnama edited by Thackston in 2002 may contain the Gurkani material.