You'll find people on both sides of this, and we can argue about what's necessary all day long.
I'll just say this, the day you have an interview, later that day or the next morning the entire team gets together to talk about you and will score you.
Thank you letters, either hand written or even by email, are rarely a decision-changer. I've asked partners that I worked for how they view letters and emails, and they said letters are a bit strange (usually because they check mail maybe once every few weeks, or whenever they get into the office) but not in a bad way. Emails are also nice gesture from candidate, but NEITHER has made them consider giving an offer when they initially rejected them.
Just anecdotal of several partners I used to work for, but in this case timeliness (email) is more important than quality/completeness/effort (written note), and neither is particularly effective at turning a no into a yes… although it is polite.
My own experience: Of the internship/full time offers I've gotten, around half of them called me before I got home that night to send a thank you email.