Cooking bolognese the day before. How cool does it have to be before refrigerating?
You want to cool down any food as quickly as possible to avoid food borne illnesses. When you are done cooking it, spread it out in a baking dish(es) because it will cool faster that way. Put it in the refrigerator UNCOVERED and when cool store in however you choose, covered. When I am in a bind for time, I also set the containers on ice.
Transfer from cooking pot to a cold pot, let sit until room temp then put in refrigerator. It will taste much better the next day, bring up to a slow simmer and serve.If in a big hurry then put the pot in an ice bath. Best to take your time and enjoy a glass of wine that will be left over from making the sauce!
I had to get a food handler's card to help out at my brother-in-laws barbecue restaurant because he was in a bind. US food safety specifically says do not let food sit out until reaching room temp, but to follow the procedure I outlined. Just sharing what the science says.
In total, you have 6 hours to cool food to 40 degrees or below. The first two hours need to get it to at least 70 degrees, so it it's something dense like a bolognese, definitely place it in an ice water bath. I also keep former beverage bottles filled 3/4 full with water in the freezer to use as ice paddles, which will cool almost anything very quickly.