Finding work this ongoing summer

I'm a rising sophomore at a target university. I had a finance internship for this summer secured but it fell through the cracks and now I'm half way through the summer and internship-less. I want to differentiate myself this coming PE and IB cycle from the horde of other applicants and I think having something to show for this summer would help. I was thinking of email/linkedin spamming every senior associate, VP, director and MD that I can find at high profile firms in my city. My email would open something like: "I am writing to you to see if [FIRM NAME] is interested in taking an intern in its [SECTOR/COVERAGE/PRODUCT] team for this ongoing summer." Do you guys think this might work? Do any of you have better ideas? Email templates to copy? I don't have any connections to bail me out here.