United Technologies is among the country’s biggest military contractors, producing engines for the Pentagon’s most advanced fighter jets and receiving more than $5 billion annually from the federal government. That equals 10 percent of the company’s revenue.

The size of the federal government’s dealings with United Technologies has also caught the eye of legislators on Capitol Hill, like Senator Joe Donnelly, Democrat of Indiana.

“It’s unfair to ask the same workers who have been laid off to pay tax dollars that will go to the company that fired them,” he said. “We’re in this together as Americans. When our workers succeed, our economy succeeds and our defense contractors succeed.”

Senator Donnelly is pushing for the government to consider outsourcing as a factor in deciding which companies receive federal contracts.

Kenneth G. Dau-Schmidt, a professor of labor and employment law at the Maurer School of Law at Indiana University, said he also thought that Mr. Trump “could get a win here,” adding, “Because they are a defense contractor, the federal government has some leverage.”

“Whether he can do something that benefits the working class in general is a different story,” he said. “The underlying problems are very hard to address. Trying to hold back the economic tide of automation, and the loss of middle-class manufacturing jobs, is something I’m not sure anybody can do.”

While Carrier is best known for its air-conditioners, it also sells a variety of other heating and cooling equipment for homes and small businesses, like the furnaces and fan coils made at the Indianapolis factory.