Whether Christ should have been tempted in the desert?

Objections

Objection 1 : It would seem that Christ should not have been tempted in the desert. Because Christ wished to be tempted in order to give us an example, as stated above (Article [1]). But an example should be set openly before those who are to follow it. Therefore He should not have been tempted in the desert.
Objection 2 : Further, Chrysostom says (Hom. xii in Matth.): "Then most especially does the devil assail by tempting us, when he sees us alone. Thus did he tempt the woman in the beginning when he found her apart from her husband." Hence it seems that, by going into the desert to be tempted, He exposed Himself to temptation. Since, therefore, His temptation is an example to us, it seems that others too should take such steps as will lead them into temptation. And yet this seems a dangerous thing to do, since rather should we avoid the occasion of being tempted.
Objection 3 : Further, Mt. 4:5, Christ's second temptation is set down, in which "the devil took" Christ up "into the Holy City, and set Him upon the pinnacle of the Temple": which is certainly not in the desert. Therefore He was not tempted in the desert only.