How long after a phone interview for a top level civil service position should you email the interviewers?

Is it appropriate to follow up an interview for a top level government position with a thank you email ? Particularly, if the interviewers were rather stiff and formal ? Does it make the candidate for the job look weak or professional ? How long should one wait before emailing the interview committee ?

How long after a phone interview for a top level civil service position should you email the interviewers?
Don't E-mail, use a professional looking typed letter, thanking them.