TEHRAN — The text message, received as the deadline for nuclear talks was expiring, gave Fatemeh Moghimi a thrill she had been waiting years to feel. “The deal,” it read, “was done.”

It took Ms. Moghimi, the owner of a leading trucking company, a second to absorb the news. When she did, she recalled recently in her Tehran office, she fairly screamed to herself, “We’re in business!”

As it turned out, the message was a bad joke, and instead the nuclear negotiations were extended for seven more months — bad news for Iran’s battered, inflation-ridden economy. But Ms. Moghimi was unfazed. “I’m not giving up hope,” she said with a smile. “It is going to be over soon. It is as if the sun is peeking through the clouds after a terrible rainstorm.”

Ms. Moghimi’s unyielding optimism, shared by many top businesspeople here, was dented briefly last month when nuclear negotiators agreed to a second extension of the talks without even a framework for further negotiations. But it is almost an article of faith in business circles that the latest extension is only the postponement of an inevitable thaw between Iran and the rest of the world.