Does John's Gospel mention Jesus' temptations?
No, John's Gospel never mentions Jesus' temptations. The three Synoptic Gospels record His temptations because they deal primarily with His humanity as the Son of God, while John presents Him from the perspective of His deity and therefore omits the temptations.
Les explains that in the three Synoptic Gospels, they all record His temptations because that was dealing primarily with His humanity as the Son of God. John doesn't deal with the temptations, and never mentions them. Another difference is His agony in the Garden and how He sweat drops of blood. All three of the Synoptic Gospels record it, but John doesn't. Why? Because these three are dealing primarily from His human side, while John is looking only from the fact that He is God. So John's Gospel omits the temptations because it focuses on His deity.