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