From a chemistry/thermodynamics standpoint, the larger the mass of ice cream, the longer it will take to refreeze.
The same principle applies to why a larger ice cream mass takes longer to melt. For example, a medium oreo blizzard from Dairy Queen has melted to the consistency of soft-serve ice cream.
I’d recommend freezing it for 20 to 30 minutes to get it to the same temperature and firmness as when you first bought it.
Despite only being gone for a 10-minute trip with the ice cream, I just purchased a medium oreo blizzard an hour ago, and it still needs to be kept in the freezer after 20 minutes.
Even though it’s not recommended to refreeze melting ice cream, it could vary depending on how much ice cream you have.
Because it will take longer than a commercially prepared product, you will alter the structure of the water crystals in the ice cream.
The faster the water crystallizes, the smaller the water crystals get—the creamier the product, the smaller the water crystals.
Consider ice cream frozen with liquid nitrogen. There’s also the possibility of bacterial development throughout this time.
It is just beginning to liquefy and will be firm enough to consume in about an hour. A good, firm freeze takes three hours.
After that, it’s not worth putting back in the fridge. Because ice crystals form during the refreeze, the texture will be gritty. “There’s just one way to cope with melting ice cream,” my grandmother used to remark.