thermodynamics - Relationship between degrees of freedom and heat capacity and absolute zero?

The Wikipedia article on heat capacity indicates that there is a relationship between the number of degrees of freedom and the heat capacity. I understand this in terms of the equipartition theorem but how I can't understand how this can be used to explain that heat capacity must go to zero as absolute temperature goes to zero (since here equipartition theorem will not hold). So please can someone intuitively explain this to me?