In most cases, you should send a thank you letter after a phone interview. This has become common in many circles for higher paying careers, and even if it isn’t common in the industry you are interviewing for, it may set you apart from other applicants. If you interviewed by more than one person, you should send a separate letter to each individual.
There are rules for sending a proper thank you letter that you will want to follow to make a good impression. First of all, be sure that you know the interviewer's name as well as the correct spelling before sending your letter. Addressing the letter with the wrong name or a misspelled version of the correct name will not make you look good. If you aren’t sure of the name, call and ask someone else in the company.
Most times, a simple card with a brief letter written inside will be sufficient. Don’t make it too long — just include a simple thanks for the person's time as well as your name signed at the bottom. It is now generally acceptable to send an email thank you note, and you should do this in the same way as a handwritten card. That said, your interviewer may be flattered that you took the time to hand write a note, since it takes more time and effort to do so.
If you are mailing the letter, don’t wait too long after your phone interview. Many individuals may have interviewed for the same job, and you will want to mail the letter quickly enough for the person to remember you clearly. This will also help ensure that he or she gets the note before making a hiring decision. It is not usually appropriate to send a gift along with your thank you letter.
Not all employers expect a thank you letter after a phone interview, but if you are unsure, err on the side of caution and send one anyway. It is better to be polite even when it's not expected than make a bad impression if it is. If applicable, mention something you spoke about your interview to show that you are attentive and pay attention to detail. This will also give your interviewer a better reminder of who you are.