the Devil used the Temptation to make Christ prove His divinity as revealed in the Baptism

Jesus' hunger during the Temptation disproved the claim , at Baptism, that God was pleased with him

both were physical experiences of Jesus at the very beginning of his public ministry

the same Spirit which fell on Jesus at Baptism also tempted him in the widerness

The Spirit of God which fell in Jesus at Baptism left Him for a while, thus allowing the devil to tempt him