The coldest Iowa caucuses in history arrive Monday night amid expectations that Republicans in the state will put former President Donald J. Trump on the march to a third G.O.P. presidential nomination.

The battle for second place, hard-fought between Gov. Ron DeSantis of Florida and Nikki Haley, the former governor of South Carolina, will anoint Mr. Trump’s closest rival ahead of the New Hampshire primary election and beyond.

The stakes for Iowans are high. Mr. Trump is pursuing a return to the presidency despite — or perhaps because of — 91 felony counts from four criminal prosecutions, a looming fraud judgment that could decide the fate of his New York real estate empire and a pending decision on the defamation of a woman he has already been held liable for sexually abusing.

His opponents have implored Republican voters to move past the “chaos” and controversies of the Trump era and pick a different standard-bearer to go up against President Biden, who beat Mr. Trump in 2020. Iowans will render the first verdict on those entreaties.