Going to be difficult given those temps. Just too darn cold for fermentation to happen. Is the day really 56 and colder than night temp or is that a typo?

Instructions read: Store at 70 degrees to 75 degrees while fermenting. At temperatures between 70 and 75F, kraut will be fully fermented in about 3 to 4 weeks; at 60 to 65F, fermentation may take 5 to 6 weeks. At temperatures lower than 60F, kraut may not ferment. Above 75F, kraut may become soft.

Can't you rig up some sort of warmer spot somewhere in the house? Like a corner of a closet shelf with a light bulb to provide heat or even an insulated cooler with some insulation?

Dave

I keep the heat off during the day in the house. That is why the day is colder. Other temps are for the garage that gets some heat at night too.

I guess fall or spring is best for making it.