The following is a map between Isaiah 38 and Second Chronicles. The key matches are Hezekiah's Illness and Temple.
13 Isaiah 38:1-8
1In those days was Hezekiah sick unto death. And Isaiah the prophet the son of Amoz came unto him, and said unto him, Thus saith the Lord, Set thine house in order: for thou shalt die, and not live.
2Then Hezekiah turned his face toward the wall, and prayed unto the Lord,
3And said, Remember now, O Lord, I beseech thee, how I have walked before thee in truth and with a perfect heart, and have done that which is good in thy sight. And Hezekiah wept sore.
4¶Then came the word of the Lord to Isaiah, saying,
5Go, and say to Hezekiah, Thus saith the Lord, the God of David thy father, I have heard thy prayer, I have seen thy tears: behold, I will add unto thy days fifteen years.
6And I will deliver thee and this city out of the hand of the king of Assyria: and I will defend this city.
7And this shall be a sign unto thee from the Lord, that the Lord will do this thing that he hath spoken;
8Behold, I will bring again the shadow of the degrees, which is gone down in the sun dial of Ahaz, ten degrees backward. So the sun returned ten degrees, by which degrees it was gone down.
38 Second Chronicles 32:24-26
24¶In those days Hezekiah was sick to the death, and prayed unto the Lord: and he spake unto him, and he gave him a sign.
25But Hezekiah rendered not again according to the benefit done unto him; for his heart was lifted up: therefore there was wrath upon him, and upon Judah and Jerusalem.
26Notwithstanding Hezekiah humbled himself for the pride of his heart, both he and the inhabitants of Jerusalem, so that the wrath of the Lord came not upon them in the days of Hezekiah.
*Unlike other places in Isaiah, this match is a known parallel passage between Isaiah 38 and Second Chronicles 32. Many Bibles cross reference these passages with a note in the section heading.
13 Isaiah 38:9-15
9¶The writing of Hezekiah king of Judah, when he had been sick, and was recovered of his sickness:
10I said in the cutting off of my days, I shall go to the gates of the grave: I am deprived of the residue of my years.
11I said, I shall not see the Lord, even the Lord, in the land of the living: I shall behold man no more with the inhabitants of the world.
12Mine age is departed, and is removed from me as a shepherd's tent: I have cut off like a weaver my life: he will cut me off with pining sickness: from day even to night wilt thou make an end of me.
13I reckoned till morning, that, as a lion, so will he break all my bones: from day even to night wilt thou make an end of me.
14Like a crane or a swallow, so did I chatter: I did mourn as a dove: mine eyes fail with looking upward: O Lord, I am oppressed; undertake for me.
15What shall I say? he hath both spoken unto me, and himself hath done it: I shall go softly all my years in the bitterness of my soul.
38 Second Chronicles 36:15-19
15And the Lord God of their fathers sent to them by his messengers, rising up betimes, and sending; because he had compassion on his people, and on his dwelling place:
16But they mocked the messengers of God, and despised his words, and misused his prophets, until the wrath of the Lord arose against his people, till there was no remedy.
17Therefore he brought upon them the king of the Chaldees, who slew their young men with the sword in the house of their sanctuary, and had no compassion upon young man or maiden, old man, or him that stooped for age: he gave them all into his hand.
18And all the vessels of the house of God, great and small, and the treasures of the house of the Lord, and the treasures of the king, and of his princes; all these he brought to Babylon.
19And they burnt the house of God, and brake down the wall of Jerusalem, and burnt all the palaces thereof with fire, and destroyed all the goodly vessels thereof.
13 Isaiah 38:16-20
16O Lord, by these things men live, and in all these things is the life of my spirit: so wilt thou recover me, and make me to live.
17Behold, for peace I had great bitterness: but thou hast in love to my soul delivered it from the pit of corruption: for thou hast cast all my sins behind thy back.
18For the grave cannot praise thee, death can not celebrate thee: they that go down into the pit cannot hope for thy truth.
19The living, the living, he shall praise thee, as I do this day: the father to the children shall make known thy truth.
20The Lord was ready to save me: therefore we will sing my songs to the stringed instruments all the days of our life in the house of the Lord.
38 Second Chronicles 36:20-21
20And them that had escaped from the sword carried he away to Babylon; where they were servants to him and his sons until the reign of the kingdom of Persia:
21To fulfil the word of the Lord by the mouth of Jeremiah, until the land had enjoyed her sabbaths: for as long as she lay desolate she kept sabbath, to fulfil threescore and ten years.
13 Isaiah 38:21-22
21For Isaiah had said, Let them take a lump of figs, and lay it for a plaister upon the boil, and he shall recover.
22Hezekiah also had said, What is the sign that I shall go up to the house of the Lord?
38 Second Chronicles 36:22-23
22¶Now in the first year of Cyrus king of Persia, that the word of the Lord spoken by the mouth of Jeremiah might be accomplished, the Lord stirred up the spirit of Cyrus king of Persia, that he made a proclamation throughout all his kingdom, and put it also in writing, saying,
23Thus saith Cyrus king of Persia, All the kingdoms of the earth hath the Lord God of heaven given me; and he hath charged me to build him an house in Jerusalem, which is in Judah. Who is there among you of all his people? The Lord his God be with him, and let him go up.