Conductivity of electrolyte solution

I found a relationship online between the conductivity of electrolyte and current.


$$i = F \sum\_i z\_i N\_i = F^2 \left( \sum\_i z\_i^2 u\_i c\_i \right)\nabla\phi = -\kappa\nabla\phi \qquad \kappa = F^2 \sum\_i z\_i^2 u\_i c\_i$$


This equation is hard for me to follow.
I get what most of the variables mean and I am guessing that $\Delta\phi$ is the potential difference. However, I thought that the conductivity was also related to temperature, which I do not see in the equation. 


It has been a struggle for me to find results on the internet to relate conductivity and current together. Can someone help me and tell me if this equation is right.


Also, this equation is true for dilute solutions, what will the equation be for concentrated solutions (solutions near $\pu{1 M}$)?


Also, how would you calculate the potential gradient?


