You have to run transient HT analysis to use temperature dependent properties.  Steady state implies that everything has "settled".

Garland E. Borowski, PE
Borowski Engineering & Analytical Services, Inc.
Lower Alabama SolidWorks Users Group
Magnitude The Finite Element Analysis Magazine for the Engineering Community

That does not sound right. Steady State HT can have Thermal-conductivity that is dependent on the temperature.  You may have to use Nonlinear Heat-transfer but it is still steady-state.

I didn't say "non-linear"...I said transient.  Steady State HT is generally used to determine termperature gradients through materials thicknesses, heat dissipation through convection, heat paths through conduction, a variety of things, but it is done with applied temperatures and linear materials.  This information is useful for times when the operating parameters are known or you are analyzing for some specific point in time.  Steady State doesn't have a "time" component to input unless I'm missing something.

Transient HT is used for, perhaps, equipment start-up where heat inputs vary with time.  Nothing is necessarily "non-linear", but you have a time-dependent  component to the analysis.  The event you are analyzing occurs over a period of time and as things "heat up", you want to change the thermal conductivity.  This is generally done with a piecewise linear curve much like you input a varying modulus for structures.

Unless I'm missing something, the difference is much like performing a linear analysis vs. a dynamic analysis.  Both are still linear, but only the dynamic analysis has a time-dependent component.