The coming-of-age drama about 17-year-old “Baby” Houseman and Johnny, a dance instructor, at a vacation resort in the Catskill Mountains was an immense movie hit in 1987 — making it a logical choice to become a stage musical today. It got its start in Australia in 2004, then toured to numerous North American cities from 2006 through 2008. It hasn’t made it to Broadway yet, but it has entertained audiences in Chicago, Boston and Los Angeles. Now it will be heating up the Aronoff for two weeks: Get ready to sing along to “(I’ve Had) the Time of My Life.”