While on the cross for three hours, after all the sins were laid upon him Jesus cried out that God forsook him (looked away, breaking fellowship). After nearly 6 hours on the cross Jesus said that He entrusted His spirit into the Fathers hands before He died. He was totally restored before He died. His Spirit was not committed into anyone’s hands, but the Father’s.
So there is no possibility of him going to hell for any reason of completing the sacrifice or punishment. He did finish on the cross everything that was needed for salvation. If Jesus went to Hell this means the Father did not accept His sacrifice, but instead rejected it.
While Jesus was on the cross He promised the thief on the cross next to him that he would be with Him in paradise that very day (Luke 23:43). If the thief was not in paradise with Him but would have entered into suffering with Jesus and Jesus lied. Paradise was still in the earth called Abrahams bosom until Christ raised and went to heaven (then he took those saints with him to heaven Eph.4:8).