Reading in Deuteronomy:
Jesus quotes from chapter 8 when tempted. In Deut 9:9 Moses fasts 40 days and nights, no bread or water, just like Jesus does in the wilderness. It's as verbatim a quote as you're going to get, and I think the Gospel writers intended the connection.
Moses fasts to intercede for Israel, so I think we ought to add this to what's going on in Jesus' temptations, too. He is not only preparing for His future ministry. He is already interceding with God to spare Israel their past offenses.