I read it ages ago and never have been able to find it again.
It's a old fic, but the premise is that Inuyasha is going into a heat/rut and is trying to stay away from the village to protect Kagome from himself. At the same time fearing going to far away, he stays closer to the village than is safe. That's where Kouga comes in to visit- he ends up losing a fight because Inuyasha is more feral and stronger at the moment and this makes him the beta of the two. So while Inuyasha is out of his mind because of the heat- he's working on pure instinct and Kouga ends up being his partner. They basically are living in the woods where Inuyasha has set up shop and Kouga is only safe from Inuyasha's attack at one point because he has Inuyasha scent all over.
I vaguely remember details like Kouga actually sleeps deeply for the first time in years because he's no longer the alpha and that when his two wolf friends come by he sends them away by acting like he's mad at them.
If anyone can remember this fic I would greatly appreciate any info.
Tags: character: inuyasha, character: kouga