No. There's nothing in the film/s that indicate why Han came back other than the exchange that occurs shortly after.
LUKE: I knew you'd come back! I just knew it!
HAN: Well, I wasn't gonna let you get all the credit and take all the reward.
Luke and Han look at one another, as Solo playfully shoves at Luke's face. Leia moves in between them.
LEIA: (laughing): Hey, I knew there was more to you than money.
We're just left to assume that he changed his mind after having left his friend to fight the Death Star on his own.
For a better explanation we need to turn to the novels. The new Junior Novelisation adds a little bit of additional speech.
Han shrugged. “Well, I wasn’t gonna let you have all the credit!”
Chewbacca growled behind Han, giving the captain a little shake.
“All right, all right, and because we wanted to make sure you got out of this mess in one piece!” Han said. “How does it feel to be a hero?”
As does the original trilogy novelisation written by Alan Dean Foster George Lucas
“I knew you’d come back,” Luke was shouting, “I just knew it! I would’ve been nothing but dust if you hadn’t sailed in like that, Han!”
Solo had lost none of his smug self-assurance. “Well, I couldn’t very well let a flying farm boy go up against that station all by himself. Besides, I was beginning to realize what could happen, and I felt terrible about it, Luke—leaving you to maybe take all the credit and get all the reward.”