well, hihihi, we dont know the next reaction from Naruto because after we saw Sakura thanked him, Kishimoto cut it. He left that moment cliffy, just like so many NS hint. It ended mysterious lol.
Imagine if he revealed that Naruto hugged her back, or at least, for normal respons, he patted her back, or smiled back, or maybe he thanked her for worrying him. (if thats happened, imagine how much people said that finally theres mutual interaction of caring, some said NS canon, then ppl thought the drama already over, the suspense stopped)
We dont know the next gesture from Naruto because Kishimoto cut it. But 615, Hinata had her hand in his cheek, then Naruto hold it back, transfered the cakra, then its done. Kishimoto didnt left it cliffy. It's clear. Naruto just did it for a purpose.
Btw, sorry for my bad english