For a variety of opinions on where the second test took place, see Joachim Jeremias, “Die ‘Zinne’ des Temples (Mt 4.5; Lk 4.9),” Zeitschrift des deutschen Palästina-Vereins 59 (1936), pp. 195–208. The Greek to pterygion tou hierou is not an architectural term. Apparently “wing” was chosen precisely because it evoked divine protection (Gerhardsson, Testing of God’s Son, p. 59).