Only some selected items can get the (cold) tag. If there is an item that can be both hot and cold, that’s a bug as both those use the same counter.
The bugs with cooling are probably the result of it only processing items every 10 minutes. As a result, items will not get cooled until the next 10 minute interval hits. This includes (hot) items.
A simple fix would be to force fridge processing when inserting the item.
A downside would be that you could just drop stuff into the fridge for a turn then have it cooled immediately. You can do that already, but at the moment you have to sync it with the 10 minute interval that depends on item’s birthday, making it hard to predict.