He also didn't go to heaven that day either.
Nobody went to Heaven until Jesus led captivity (O.T.saints (believers)) from Paradise, when He was resurrected. They were all, including the thief on the cross, preserved in Paradise, under the Old Testament until the resurrection. The thief on the cross died before the resurrection, as the soldiers broke the legs of those crucified with Jesus, so they would die more quickly, before the Sabbath. So, then, the thief was with Jesus that same day, in Paradise, awaiting the resurrection, when he, along with all believers throughout the previous history, were translated from Paradise to Heaven.