According to current state law, the special election for the vacant Senate seat will be held in 145-160 days, which would mean either January 19, January 26, or February 2.
The party primaries for that election must be held six weeks earlier, which would be either December 8, 15, or 22.
I am getting informed speculation, however, that there may be a proposal to change the law -- aside from any change concerning a temporary appointment.