Mr. Trump’s advisers hope that he can get under Mr. Biden’s skin on Thursday at the debate in Nashville, which will begin at 9 p.m. Eastern. But they have also urged the president not to interrupt Mr. Biden repeatedly, after a first contest in which Mr. Trump constantly hectored his rival — and Mr. Biden told him to “shut up” — as the evening spiraled out of the moderator’s control.

The president has signaled he intends to focus on Mr. Biden’s son Hunter and his business dealings, after an unsubstantiated New York Post report on that subject. But some advisers fear he will not be able to control himself and will attack the younger Mr. Biden in a way that engenders sympathy for the Biden family, a dynamic that unfolded in the first debate when Mr. Trump mocked Hunter Biden’s history of battling drug addiction.

“The president, in order to have a successful debate, has to go on offense without being offensive,” said Brett O’Donnell, a Republican strategist who has coached candidates in debates. “The American people care more about their own family than they do about the family of Hunter Biden. Especially during the pandemic.”