Thermae Romae (2012)

Lucius Modestus, ancient Roman bath architect, has lost his job. The one way he can win it back is by creating a bath that nobody has seen before, and, by pure chance, ends up slipping through time to Japan in 2012. There, he discovers the wonders of Japanese bath technology, incorporating it into his own designs, but must face the challenges of the succession of the emperor, his home life, and his new hot spring-based friends, including manga artist meet-cute Mami.