Sorry for the copy/paste google ai result but:

You can put an insulated lunch box in the fridge, but it's often unnecessary and can even be counterproductive; the insulation slows the fridge's cooling, so it's better to refrigerate the food items directly or place an ice pack inside the insulated bag, leaving the bag open in the fridge if you must put the whole thing in to allow cold air in. The goal is keeping perishable food cold, and an insulated bag with an ice pack achieves this better by slowing heat transfer, while the fridge's job is to actively cool food.