Why does it say "El ha'Kir"?
Radak: It was in order to have intent in his prayer 1 . He was astounded - why is Hashem shortening his life? He was only 39 years old when he fell ill!
Radak citing Targum Yonasan: [He put his face] to the wall of the Beis ha'Mikdash.
Malbim (Yeshayah 38:2, based on R. Yehoshua ben Levi (Brachos 10b)): He prayed mi'Kiros (from the deep chambers) of his heart -- "Me'ai Me'ai Ochilah Kiros Libi" (Yirmeyah 4:19).
R. Levi (Brachos 10b): He based his prayer on a wall. He said, You revived the son of the Shunamis woman, because she built one small wall (to make a lodging for Elisha). My ancestor (Shlomo) covered the entire Heichal with gold and silver, all the more so [You should extend my life in his merit]!
Malbim (Yeshayah 38:2): This was lest people of the household distract him.
