As stated in this answer for a somewhat related question:
The ideal refrigerator temperature is 35°F (1.6°C). You're not hugging the danger zone like you would be at 40°F (4.4°C), and you're distancing yourself sufficiently from 32°F (0°C) that you don't freeze half the stuff in your refrigerator. That said, the temperature within your fridge can vary rather significantly with normal usage.
The reason for the quote is that most domestic refrigerators are able to be set to a temperature of less than 40ºF. As you are not talking about domestic but it sounds more industrial/professional, I doubt you would have a refrigerator that can't store at a temperature below this.
Therefore I would imagine storing it in the fridge would be fine and more convenient than the ice bucket suggested.
However the temperature within different areas of the fridge can vary depending on how frequently it is accessed (which is why you shouldn't keep eggs or other easily spoilable foods in the fridge door) so this could potentially be a problem depending on your exact situation, how frequently it is opened and where in the fridge you keep the batter.