Final answer:
Augustus' grandsons whom he adopted as heirs were Gaius and Lucius, and they were intended to continue the Julio-Claudian Dynasty, but both died young.
Step-by-step explanation:
Augustus' grandsons whom he adopted as heirs were Gaius and Lucius. The dedicatory inscription of a temple honored them as "To Gaius Caesar, son of Augustus, Consul; to Lucius Caesar, son of Augustus, Consul designate; to the princes of youth." These grandsons were hoped to continue the Julio-Claudian Dynasty following Augustus, but unfortunately, both died young before they could ascend to the role of emperor, leading to a different succession of heirs.