Why do Drude/Sommerfeld models even work? Sommerfeld's model for the electrons heat capacity works well on the extremes of high and low temperatures.
While the model is quantum and assumes the electrons are an ideal gas, the reality is VERY different, with the electrons bounded to protons and having interactions between them.
So why do this model even work?
EDIT:
Original question was asked about Drude's model as well, but answering the question about Sommerfeld's model will answer why Drude's model works at high temperatures since quantum effects will be neglected.
 A: Landau Fermi liquid theory shows that excitations in metals can be treated as independent particles. These particles have mass, dispersion relation and other characteristics very different from those of "free electrons" that we could have predicted from simple band structure calculations, but this hardly metter for Drude-Sommerfeld theory, where many parameters are phenomenological (mass, scattering time/length, etc.)
While the theory works remarkably well for many materials, there are well-known cases where it is not obeyed (non-fermi liquid behavior):

*

*In superconducting regime

*In one dimension (Littinger liquid)

*In magnetic alloys (Kondo effect)

Remark
After re-reading the question, I think that my answer may imply the background that the questioner does not have. I recommend therefore looking up questions on the band structure and the difference between insulators and metals, e.g. here and here.
A: 
Drude's (and consequently Sommerfeld's) models for the electrons heat capacity works well on the extremes of high and low temperatures.

Do they?
The two models give very different results:

*

*Drude's model is that of a classical gas: $c_v = \frac{3}{2}nk_B$ (See Ashcroft and Mermin Chapter 1, Section "Thermal Conductivity of a Metal".)

*Sommerfeld's model is that of a free electron gass: $c_v = \frac{\pi^2}{3} \left(\frac{k_B T}{\epsilon_F}\right) nk_B$ (Ashcroft and Mermin Eq. 2.81).

Drude's model isn't temperature dependent, and it does not work well at the extreme of low temperature.
Could you clarify which models you are thinking of?
