I'd think of it this way:
not any degrees = zero degrees
The only time I think I would use "zero degree" is when that phrase is actually used as an adjective to modify a noun. For example:
- a zero degree day = a day on which the temperature is zero degrees
Haohaoxuexi“ And how about "A minimum of 10 minutes is / are required?"”
I would use the singular "is" because we are talking about a minimum (amount). "A minimum" is singular.