How do I get a healthcare/life science VC internship?

I'm a rising junior at a state school. I'm doing an internship right now at a tiny PE search fund, but the sector focus is a bit boring to me. I've always been excited by biotech and life sciences. I'm looking for something to do this fall and I want to get some exposure to the life science sector. 

I'm gathering some firms to cold email, but how should I go about this? Should I write up some stuff about one of their portfolio companies? Should I attach a pitch for an early-stage bioscience investment? How can I get their attention and convince them to let me intern for them despite not having a technical science background?