Temperature Dependence of The Conductivity of Electrolytic Solutions
One useful approximate relationship that can be used to predict the temperature dependence of the conductivity can be obtained by relating the electrical mobility to the viscosity.
For a $z_+:z_-$ electrolyte the limiting molar conductivity can be expressed as
$$\Lambda^\circ _m =  F^2\left(\frac{z_+^2\nu_+}{f_+} + \frac{z_-^2\nu_-}{f_-}  \right)$$
where the $f_i$ are frictional coefficients  for each ion, z is the ionic charge, $\nu$ is the stoichiometric coefficient, and F is the Faraday constant (for instance, for $\ce{Al2O3}$, $z_+=3$,$\nu_+=2$,$z_-=2$,and $\nu_-=3$.
The frictional coefficients can be related to the viscosity, for instance using Stokes' relation $f=6\pi \eta r$ for a sphere being driven through a uniform viscous medium with a low Reynold's number. From the temperature dependence of the viscosity, and assuming the ion radii are independent of T, you can derive a relation for the T dependence of the limiting conductivity:
$$\Lambda^\circ _m = \frac{F^2}{6\pi\eta (T)}\left(\frac{z_+^2\nu_+}{r_+} + \frac{z_-^2\nu_-}{r_-} \right)$$
The equations so far apply to dilute solutions where the viscosity is independent of the concentration of electrolyte and ion-ion interactions can be neglected.
Note that even simpler theories predict a somewhat complex dependence of the molar conductivity on temperature. One can however attempt to fit an expression inspired by those above, of the sort
$$\Lambda _m = A \times \eta (T)^{-1} $$
where A is assumed independent of T. This might work over a narrow T range and could be used to assess the importance of ion-ion interactions.