Yes they are linked through Indo-European temh (= to cut), which has given Latin temno (= I despise), and tempus (= time).
1) tempus is a "section (of time)".
2) Concerning temno, the link with "to cut" is not so clear, but we can say it's a way to "cut the link" with somebody.
The etymology is questioned though, and some sources associate Latin temno with IE stemb (= to crush). In that case, there would be no link between contempt and time.