Hello GrillMaster_SG86, that's a common and perfectly solvable situation! It's great that you're getting into fermentation. Let's make sure that beautiful sauerkraut is perfect for your BBQ.
Sauerkraut is a living food, and its fermentation speed is directly related to temperature. When you put it in the fridge, you are essentially pausing the fermentation to lock in the flavor and texture you like.
THE IDEAL TEMPERATURE
Without a refrigerator, your goal is to find the coolest, most stable temperature you can. The ideal "root cellar" temperature for slowing fermentation is between 10°C and 15°C (about 50-60°F). At this temperature, the kraut will continue to mature very slowly but won't become overly sour or soft in just a few days.
STORAGE TIPS
Find the coolest and darkest spot in your home. This could be a basement, a pantry, a cabinet against an exterior wall, or even a cooler with a frozen ice pack (just make sure it doesn't freeze the jar).
Ensure the cabbage is fully submerged under the brine. This is the most critical step to prevent spoilage. Any cabbage exposed to air is a risk for mold. You can use a fermentation weight, a small plate, or even a clean ziplock bag filled with a bit of brine to keep everything down.
Burp the jar. If your jar doesn't have an airlock, you will need to open it briefly once a day to release the pressure from the ongoing (but slower) fermentation. This prevents the jar from cracking.
For your weekend BBQ, a few days at a cool room temperature will be perfectly fine. The kraut will likely get a bit more tangy, which many people enjoy, especially with rich bratwurst. Enjoy the party!