An enthusiastic +1! I e-mailed a prospective supervisor in late november and she enthusiastically squeezed me in for a meeting by mid-December. It was a very productive conversation that generated a lot of great leads and application edits! Regarding the "thank-you": I sent an e-mail 3 days after the meeting and got very positive results from this! These things can be tricky to write, so I'll copy the gist of it below, feel free to appropriate!
Professor________,
I just wanted to write a quick e-mail to thank you for taking the time to meet with me last Friday. As I mentioned, I was thrilled to have the opportunity to discuss my potential academic prospects and research in ___(field of interest)___. As well, I'm always happy to speak to my positive undergraduate experience at __(undergrad institution)___.
At your suggestion, I have e-mailed Professer __(referral #1)____ and __(referral #2)__ in order to explore potential research interest alignment and the prospect of working together at __(prospective graduate university)__. While I don't expect an immediate response (as we've entered the holiday season), I do hope that this correspondence will be fruitful and I appreciate that you lent your name to these referrals!
I hope that you have a pleasent holiday season. I'd be more than happy to keep you abreast of developments, as your time and interest dictates. At the very least, I will let you know the outcome of my applications.
Thank you again for your insight and encouragement!
Warm regards,
___(Surefire)___
___(contact info)___
A few points: I was sure to mention the meeting date and to re-iterate my research interests, to re-acquaint her with our meeting (I assumed that she had met with a variety of prospective and current students, it WAS the pre-holiday crunch!). As well, I alluded to a bit of conversation that we had regarding my undergraduate institution and some specific professors. This part of our conversation was light-hearted and likely unique (my undergrad uni department was small, but we were both connected to it), so I figured that that might be a good mental cue for which I could be remembered. I was sure to follow-up promptly on her suggested leads (profs in similar fields who might serve on my dissertation committee or vouch for me on adcomms) and made note of this in the e-mail. This has the dual benefit of showing her my initiative and letting her know that her advice was being utilized (so she can be prepared to confirm with the recommended profs that she had in fact referred me). I thanked her specifically for "lending her name" as she encouraged me to let these other professors know that SHE had referred me (for me, this is above and beyond the realm of friendly suggestion). I ended with a suggestion for future contact and left options on the table, so she could chose to contact me again or, at minimum, she would hear from me again with an application outcome. This part was particularly important for me; as someone who has instructed university students and written reference letters and/or offered referrals and guidance, I always like to know what the outcome is. This allows me to tailor my approach accordingly and substantiates the advice I put forth. Even if this prof doesn't particularly NEED this feedback, as she is established, I want to volunteer the closure.
What happened next was interesting. I was off briefly for the holiday season and checked my e-mail infrequently, as I had managed expectations regarding any feedback at all, let alone prompt responses. I got three e-mails last week. One from the Prof that I'd met with that said, and I quote, "You are a rare student under 30 who can write a great thank-you note"; she also invited me to attend the next departmental seminar series, to get a feel for the current faculty/cohort/resources. The other two e-mails were from the profs that I had been referred to. Each had their own advice, but they had this in common: they were both positive and they both iterated some variation of, I kid you not, "oh, you're the polite __(research field)__ student that __(referring prof)__ mentioned".
So, yeah, thank-you notes! Go forth and DO them! These exchanges have some other substance to them (the actual interview went well, I was prepared, there is some great departmental fit that is apparent), but I also have no problem being known as that "polite one". I am known in a positive capacity, and this is a good start!
