It does change, but just by a smaller amount - something around 10^-5 1/K, compared to copper, which is around 10^-3 /K The value for this thermal conductivity depends a lot on the properties of the material, especially on the scattering processes of conduction electrons.

The temperature coefficient of the electrical resistivity is small in a given temperature range. After, the temperature coefficient becomes more important.

This behaviour is well understood for liquid alloys through the Faber-Ziman formalism. I wrote a synthesis on it:

Understanding the resistivity and absolute thermoelectric power of disordered metals and alloys. Jean-Georges Gasser Journal of Physics Condensed Matter (impact factor: 2.55). 03/2008; 20(11):114103. DOI:10.1088/0953-8984/20/11/114103

I have extended the formalism to solids. You can download the talk on researchgate (GASSER LAM14). “A general understanding of electronic transport properties in solid alloys (amorphous and recrystallized ones”) 2010-07-11 - 2010-07-16 J.-G. Gasser, L. Abadlia, K. Khalouk, F. Gasser, I. Kaban, T. Aboki, M. Mayoufi

What may be retained:

1) The resistivity is function of energy

2) The thermopower is the derivative of the resistivity versus energy

3) The resistivity and the thermopower have to be calculated at the Fermi energy

4) The Fermi energy changes with temperature

5) The resistivity versus energy curve presents maxima and minima

To come back to your question, when you make an alloy, the Fermi energy can fall at a given composition on a maximum (or minimum). At this composition a change of Fermi energy (due to temperature) does not change a lot the resistivity and gives a thermopower near zero. If you are on the increasing part of the resistivity versus energy curve the temperature coefficient of resistivity is negative and the thermopower is positive. If you are on the decreasing part of the resistivity versus energy curve the temperature coefficient of resistivity is positive and the thermopower is negative.

It is the inverse if the Fermi energy is near a minimum

Delete the last sentence, it is wrong:

It is the inverse if...

Some more explanations

In my talk at LAM 14 conference (power point downloadable on research gate under GASSER LAM14 ), you see p38 a typical curve of resistivity versus energy as a 1/E curve modulated by the first peak of the structure factor. The Fermi energy decreases with temperature as well as the curve itself which also decreases (the peak of the structure factor decreases with temperature). Contrarily to what one in general believes, real metals in solid state do not have a structure factor with very sharp peaks because

1) Real metals are not monocrystalline

2) Temperature induces vibrations of ions around a mean position and thus the peaks are broadened (see fig p 47)

Concentration changes the Fermi energy. The Fermi energy is in the peak of the structure factor when the valence is of about 1.7-1.9. It is more complicated with transition metals. So it is possible tu "tune" the composition in order to get the good valence in order to have a zero temperature coefficient.