I've done quite a bit of cold-emailing to reach new mentors and new clients.
One of the things I started doing a couple years ago was to offer buying someone I was cold-emailing a "virtual cup of coffee". I even played with using that in the subject of the email.
I'd say: I'm working on a new product and I wanted to see if it would be handy for them. If they have a chance to talk on the phone or Skype, I'll send over a gift certificate to Starbucks so they could get their favorite drink before the meeting.
Those emails got some nice hit rates in responses and meetings. And you can very easily buy a $5 gift cert. online from Starbucks and email it.