Specific capacity of a diatomic molecule at low temperatures

My question is: Why at low temperatures does a diatomic molecule result in the same specific heat capacity as a monoatomic at a constant volume? My understanding is that at very high temperature there are two additional degrees of freedom from the vibration between the atoms, this gives the specific heat capacity of $C_v=\frac 7 2 R$ at room temperature. Vibrational degree of freedom does not occur, so we are only left with translational and rotational. But a very low temperature it seems that rotational motion does not occur. But why?