How to go about sending open/prospective/cold applications for internships?

So...

The 2020 SA Recruiting Season is not technically over but it is pretty much over in all but name. I didn't make the best effort to get into a role and the roles I did make an effort for didn't yield much fruit. Currently I'm on a placement year (3rd out of 4 years) (till June/July 2020) doing FoF at a mid sized PB/AM. 2020 Summer is thus my last chance to get a summer internship, unless I get a Masters which I don't really want to do. My actual focus is not IBD or S&T but more towards ER, WM or AM. Since FoF is very much a dying industry with a niche skillset, I don't think my experience here will help too much with later recruiting, hence wanting a back to back summer internship.

Since most large firms have finished their recruiting now, I'm looking towards trying to get a place at smaller or non-advertising investment firms that I can hopefully get some proper equities/fixed income experience (not too bothered either way, I'm an econ student so either suits me and I'm after the core skills really).

How can I go about sending open/prospective applications to companies who haven't advertised that they're hiring an intern? Should you network first? Just send cold? How would you do a cover letter? Is this even a viable plan?

Any advice is welcome