She lives and works out here in West Texas, but lately seems to be everywhere, kicking off a series of “Global Weirding” videos, posting on Twitter and Facebook, and speaking anywhere from local churches to international conferences. Last week, she appeared at the White House to discuss climate change with President Obama and the actor Leonardo DiCaprio at the first South by South Lawn ideas festival.

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When she started her work spreading the word about climate change in Texas, very few people in the Lone Star State believed it was happening, and even fewer believed that people were causing it. Since then, acceptance has grown: A 2013 poll by the Yale Program on Climate Change Communication found that seven in 10 Texans agree that climate change is real, though fewer than half said humans were the major cause.

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Dr. Hayhoe has come to prominence in part because she is just so darned nice. It would be too easy to chalk that up to her Canadian background — she says it does help explain her commitment to finding consensus — and she has found that she gets her science across more effectively if she can connect with people personally. In a nation seemingly addicted to argument as a blood sport, she conciliates. On a topic so contentious that most participants snarl, she smiles. She is an evangelical Christian, and she does not flinch from using the language of faith and stewardship to discuss the fate of the planet

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“Katharine Hayhoe is a national treasure,” said Anthony Leiserowitz, the director of the Yale Program on Climate Change Communication. He said that she combined powerful communications skills, world-class scientific credentials and an ability to relate to conservative religious communities that can be skeptical about the risks of a changing climate.

Gavin Schmidt, a NASA climate scientist, said in an email that Dr. Hayhoe’s faith is an important factor, because “people can accept unwelcome truths much more readily if they come from within, rather than from outside, their community/family/group.”

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While some climate warriors treat those who are not inclined to believe them as dupes or fools, she wants to talk. “If you begin a conversation with, ‘You’re an idiot,’ that’s the end of the conversation, too,” she said over tacos at a Tex-Mex restaurant, having ordered in the fluent Spanish she picked up during her parents’ missionary service in Colombia. She is 44, but seems younger — someone who speaks with authority but can punctuate a statement about a surprising scientific fact with a wondering, almost giggly, “Isn’t that crazy?”

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Now, in a presidential election race with high stakes for responding to climate change — Donald J. Trump has called global warming a hoax and would reverse deals that President Obama has spearheaded to reduce greenhouse gas emissions, while Hillary Clinton has called for continuing along Mr. Obama’s path — there is room for many approaches. Some will rally the troops; she will reach out to the quiet people in the middle, the undecided, who might listen.

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​Some in the climate community argue that congeniality like Dr. Hayhoe’s can be counterproductive, especially when well-funded deniers of climate science spread disinformation and vituperation. Michael E. Mann, a climate scientist and author at Pennsylvania State University, said locking horns has its place, too: “There is also a role for an approach that takes bad actors to task, naming names when it comes to the worst climate villains, those who are knowingly misleading the public and policy makers. Such an approach doesn’t necessarily endear oneself to the hard-core climate change deniers, but it does help to expose the deceit, and in my view it is important for the public to know about that.”