I am re-drafting my cover letter for the tenure track faculty positions in the U.S. While I was finishing my dissertation, I quickly moved to a new research direction. Although I can make the case of how my new research direction grows out of my dissertation, I wonder when do people stop talking about their dissertation in the cover letter? Or must the cover letter contain a dissertation paragraph?
My usual advice about cover letters and vitas is to include everything that you can include "with a straight face". A some point you stop putting your high school awards, because it's too embarrassing to mention them; at some later point you stop putting minor honors from your undergraduate studies; etc.
If you are a recent PhD and are applying for tenure-track positions, you should certainly mention your thesis, unless you have so much other research that it is no longer relevant.
But you do not necessarily need an entire paragraph. Just now, I looked up two successful cover letters of mine. One had a single sentence about my thesis (for a research post-doc position). One had two sentences, the second of which just said that my work could be suitable for undergraduate research (this letter was for a tenure-track position). At least in my field, we usually submit a longer "research statement", and so there is little need to go into depth about research in the cover letter.
You are mostly hired for what you are doing now, so you should avoid the impression that you are unsteady, and your interest shift every other year. However, there will be some members of the committee who are not from your current area. If one of them is interested in your Ph.D. topic, this might be a big bonus for you. So you should mention your Ph.D. topic unless your results are mediocre, or so much time has passed since your Ph.D. that a faculty member interested in that topic and not your current work would not see an advantage in having you in place of someone with a different Ph.D. topic. How much time this actually is depends on the subject area. In many branches of pure math this could be "never", while in applied areas of CS this could be 2 years.