Dependance of heat capacity at constant volume on temperature for solids and liquids
The molar heat capacity of classical ideal gases at constant volume is temperature independent, because there are not considered quantization steps of electronic, vibrational and rotational energy.
The molar heat capacity ideal gases in the context of quantum-mechanic-aware gas theory is not temperature independent anymore. Because the electronic, vibrational and rotational energy contribution depends on ratio of mean energy per degree of freedom $E=\frac{1}{2} \cdot k_\mathrm{B} \cdot T$ versus the energy of quantization steps.
The capacity raises as rotation energy contribution kicks in, and later vibration energy as well, and finally electronic energy, as their quantization steps grows in this order.
There is a similar temperature dependent effect for liquids and solids, where quantized vibration is essentional, especially for solids.

The classical model of ideal gas does not take into account quantum effects. By warming up of an ideal gas, the mechanical energy gets evenly distributed between energy of linear motion, bond vibration and molecular rotation, proportionally to absolute temperature.
Quantum effects, taking part in behaviour of real gases, liquids and solids affects energy distribution. Vibration, rotation or electron energy are allowed by laws of quantum mechanics to have just some energy levels.
Imagine you throw small stones upwards to a steep hill. Stronger you throw it, the higher it would stay. This is analogous to an ideal gas.
Now you try to throw such stones to open windows of a tall building. If you make weak throwing, it will not flow even to the nearest window and will fall back. Stronger and stronger throwing ( = higher temperature ) would eventually cause some stones would reach at least the 2nd floor. Later even 3rd one etc.  This is like quantization of possible energies for real gases and condensed phases.