Is it possible or feasible (for a college institution) to purchase temporary liability insurance for students who participate in temporary internship program with law enforcement agencies?

You can get insurance for almost anything. Depends on how much you are willing to pay for it. Remember Betty Grable insured her legs.

Frankly, I think it's a good idea to purchase such insurance to protect the institution.

It's possible, the students would be insured under a blanket policy (covers a group of people). Some companies only take on certain risks so you may have to shop around. If you find an independent agent (one who is not tied to a specific company) they can do the shopping for you.