David Letterman, 52, who’s had a strenuous week, revealed on a program to air Friday that he’s set to undergo heart tests today. Admitting that he suffers from “very high cholesterol” and has a family history of coronary problems (his father died of a heart attack when only in his 50s), Dave said the worst-case scenario would be to “open daddy’s rib cage . . . and I don’t want that.”