How are the stories of Hezekiah's illness and Sennacherib's attack linked? They are both in crisis and in both stories, a salvation is granted. Assyria is struck a blow and sent away. Hezekiah's illness is struck a blow and sent away as well. In Hezekiah's reprieve we learn explicitly that it is temporary. He is granted an additional 15 years. Jerusalem's reprieve will also be temporary.
"In short, the fall of Jerusalem in 587 BC is already beginning to loom up on the horizon of the narrative; it will come into direct view at the end of chapter 39, and dominate the scene from there on. Chapters 38 and 39 are not (as they might at first appear) a digression from the main drama, but an introduction to its second major movement." - Webb, p155.