Ask HN: Cold-Emailing for internships. Suggestions?

I'm currently a Sophomore in college. Now it's time to start looking for summer internships. I've been following HN for a year now and I'm very passionate about the whole startup ecosystem. I have offers from Megacorps that come to my school to recruit, but being in the Midwest, most startups dont show up to these events. I know that cold-emailing (or LinkedIn's InMail) works, but not sure as how to approach the companies I'd like to work with. I'm sure many member of this community are now on the other side of the table and probably had to do similar steps as I did, so I'd love to hear suggestions from fellow HNers.