In the last year of his life the senate voted Caesar a run of honours that no living Roman had held: a statue among those of the gods, a temple to his clemency, a couch carried in the procession of the gods at the games, and a flamen, a priest of the kind attached to individual deities, with Mark Antony named to the post. Whether that amounted to worship of a living man, or to extravagant honours that stopped just short of it, was argued at the time and is argued now. The distinction mattered enough that it appears in the justifications his assassins gave.
He was killed in March 44 BCE before the flamen was installed. Four months later his heir staged games in honour of Venus Genetrix, and a bright comet appeared for seven days. It was read publicly as the soul of Caesar received among the gods, and the young Octavian, by his own later account, was privately delighted to be able to say so. A star was added to the statue's head, and the sidus Iulium became a standing image on coinage.
The formal step came in 42 BCE, when the triumvirs had him enrolled by law among the gods of the Roman state as Divus Iulius, with a temple on the site of his cremation in the Forum, dedicated in 29 BCE. The consequence for his heir was immediate and enormous: the adopted son of a god could describe himself as divi filius, son of the deified, and did so on his coins for the rest of his life. The Roman practice of raising a dead ruler to a god by decision of the state begins here, and every later consecration follows the shape of it.