John Chrysostom

"But ye would not," He saith. "Behold your house is left desolate," stripped of the succor which cometh from me. Surely it was the same, who also was before protecting them, and holding them together, and preserving them; surely it was He who was ever chastening them. And He appoints a punishment, which they had ever dreaded exceedingly; for it declared the entire overthrow of their polity.

Homily on the Gospel of Matthew 74 ↗

Theophylact of Ohrid

But as you do not want My affection, I leave the temple empty and abandoned. From this let us learn that God inhabits the temples for our sake, but when we have forsaken God, then the temples are abandoned [by God] as well.

Commentary on Matthew ↗

Jerome

Verse 38. Behold, your house shall be left desolate. This very thing Jeremiah had already said in the person of Jeremiah: I have forsaken my house, I have cast off my inheritance: my inheritance is become to me as a lion in the forest. We see with our eyes the house of the Jews left desolate, that is, that temple which shone more brightly, because it lost its inhabitant Christ, and, desiring to seize the inheritance, killed the heir.

Commentary on Matthew ↗

Thomas Aquinas

Then the punishment follows: behold, your house shall be left to you desolate. The whole people was honored on account of Jerusalem, and Jerusalem on account of the temple; therefore it says, your house shall be left, i.e., the temple, or the dwelling; Psalm 68:26: let their habitation be made desolate. Or a house is said to be desolate when it lacks its proper inhabitant; Psalm 10:5: the Lord is in his holy temple. …

Commentary on Matthew ↗