So normally when you see k which is the conduction coefficient, it's just a number that depends on the material.
In reality though, the number might change as the temperature changes. Thats why when you go to a site to see the thermal conductivity of some materials, it'll list different numbers for different temperatures:
https://www.engineeringtoolbox.com/thermal-conductivity-d_429.htmlI think your questions are just asking you to make up some nonlinear function k(u) like k(u) = u^2+20 or some shit and then to see if your matlab model succeeds (converges) or freaks the fuck out (diverges)
part c i think you just consult a table and notice that the 25C and the 125C thermal coefficients are different. maybe you can wing it and interpolate the given values to derive a k(u) function, idk. this question is pretty stupid.