Notes from The Catholic Encyclopedia - Temptations of Christ
As our first three Gospels agree concerning the time to which they assign the
temptation of Christ, so they are at one in ascribing the same general place
to its occurrence, viz. "the desert", whereby they no doubt mean the
Wilderness of Judea, where Jesus would indeed be, as St. Mark says: "with
beasts". From St. Mark (i, 13) -- with whom compare St. Luke iv, 2 -- we
learn that Jesus Christ was tempted during the forty days which He spent in
the desert (cf. St. Augustine, "Harmony of the Evangelists", II, xvi),
so that the three onsets given in detail by St. Matthew and St. Luke are apparently
the three final assaults of Satan against Christ. The first of these assaults
is directly connected in both St. Matthew and St. Luke with the prolonged fast
of Jesus in the wilderness. The Tempter suggested to Jesus that He should use
His miraculous power to relieve His hunger, by changing into bread the loaf-like
flints of the desert. The two other assaults are given in a different order,
St. Matthew adhering probably to the order of time, and St. Luke to that of
place. The spot pointed out by tradition as the summit from which Satan offered
to Jesus dominion over all earthly kingdoms is the "Quarantania",
a limestone peak on the road from Jerusalem to Jericho. As regards the Temple's
pinnacle from which the Tempter bade Jesus cast Himself down, it was not the
top of the House of Yahweh, but probably the roof of Solomon's portico from
which, at a later date, St. James was actually hurled to the pavement below
(Eusebius, "Hist. eccl.", IV, xiii).