Trace width calculator for any material
If you have equations for (say) 1oz (34.79um) copper, simply pre-scale the equivalent current based on the resistivity and trace thickness. 

If the trace is carrying 0.5A and the material has bulk resistivity 3 times that of copper and it's 60um thick, then it's the same as a copper trace carrying 0.5 * sqrt(3) * sqrt(34.79um/60um) = 0.66A. 

Heat loss should not be affected significantly by trace thickness or resistivity.