I've actually never tried. At the time that I want to tighten the mounting screws, it is because I am annoyed at the noise right that minute. The fan is in use and the stove is hot.
I know a sensible person would just remember to take it apart next time the stove is cold, but A) I won't remember and B) Next time the stove is cold is in May sometime. I suppose I could just pull it and let the stove poot along with no fan, though. Okay, so that last one is what a sensible person would do.
See, I got there eventually!