As he tries to halt the momentum of Donald J. Trump, Gov. John Kasich of Ohio tells people they are made special by the Lord. He urges them to invite lonely widows out to dinner. He freely dispenses hugs.

Mr. Kasich’s aura of civility, kindness and positivity is so pronounced — and so at odds with the fulminations of the real estate mogul — that an anxious voter in Worcester, Mass., wondered whether he could summon the combativeness required to be an effective president.

“I worry that you’re just so nice,” the woman said.

Mr. Kasich’s colleagues in Ohio and Washington do not share that worry. In interviews, they recall a three-decade career in government punctuated by scolding confrontations, intemperate critiques and undiplomatic remarks.

Today, as Mr. Kasich makes comity a centerpiece of his long-shot bid for the Republican nomination, they describe his candidacy as an exercise in remarkable self-restraint that has managed to keep his crankier instincts mostly out of sight.