Calculating heat flux (Q) without thermal conductivity (K)

[gphsuvat]

How to calculate K or Q without one or the other?
For example, if the material is unknown (but cannot test density, or melting temperature)
how would you test heat flux?

Q=K(Th-Tc)/(x)

 

[CWatters]

In the homework section the rules require you to make an attempt to answer.

Perhaps think about other experiments that involve measuring heat or power.