There is a really good book, <em>Pierced For Our Transgressions</em> that does a nice exegetical study of how the Scapegoat is a type of Christ as it relates to penal substitutionary atonement. I highly recommend checking the book out if you can.
I don't really see the Scapegoat relating to Christ's temptation in the wilderness. For me, this is more of a parallel to the 40 years the Israelites spent in the desert, or perhaps to Elijah and Moses fasting 40 days and nights. I was listening to Michael Kruger's lecture series on the Gospels from the RTS mobile app, and he mentioned that some scholars have drawn parallels of Jesus' life to the Exodus. I'll have to go back and find those sources, but I found them to be quite interesting. Maybe somebody more knowledgeable than I can shed some light here.