I have read that Cp and Cv are independent of temperature for the case of a perfect gas whereas for an ideal gas it will vary with temperature. The variation in Cp and Cv with temperature is attributed to the activation of the additional DOFs at high temperature. Although over the normal range of temperature it can be considered almost independent of temperature.
My question is
Update :
For monoatomic gases there are no rotational DOFs. I don't know about vibrational modes. So I think the Meyer's relation will hold true at all temperatures for monoatomic gas.
Link regarding the convergence of Cp and Cv value at absolute zero temperature.