“They think it’s not going to be that big a deal,” said Amit Kumar, a professor at the University of Texas at Austin who studies well-being.

They also overestimate how insincere the note may appear and how uncomfortable it will make the recipient feel, their study found.

But after receiving thank-you notes and filling out questionnaires about how it felt to get them, many said they were “ecstatic,” scoring the happiness rating at 4 of 5. The senders typically guessed they’d evoke a 3.

To be clear — the notes in question were not your typical “thanks for the Amazon gift card.” Rather, the 100 or so participants in each of the four experiments were asked to write a short “gratitude letter” to a person who had affected them in some way. Sample letters included missives of appreciation to fellow students and friends who offered guidance through the college admissions process, job searches and tough times. In lab experiments, Dr. Kumar observed that it took most subjects less than five minutes to write the letters.