Molten lithium carbonate conductivity
The conductivity of molten lithium carbonate has been determined for vast range of temperatures (Ref.1). The abstract of which states that:


  The present communication reports the results of an investigation of the properties of surface tension, density, and electrical conductance for molten $\ce{Li2CO3}$, $\ce{Na2CO3}$, and $\ce{K2CO3}$ and some mixtures in the temperature range of $750^\circ –\pu{1000 ^\circ C}$. The surface tensions are approximately twice the values for the corresponding chlorides; the densities and electrical conductance are quite comparable to those of the chlorides. The ionic nature of the molten carbonates is examined from the physicochemical criteria based on these properties; and the mechanism of electrical transport is considered in the light of current theoretical concepts. Relative to $\ce{Na2CO3/K2CO3}$ mixtures, the surface tensions and partial molal volumes indicate but little deviation from the predictions for thermodynamically ideal mixtures.


The conductivity of molten lithium carbonate/metal carbonate mixture has also been determined for range of temperatures (Ref.2), the abstract of which states that:


  The electrical conductivities of the molten binary salt mixtures $\ce{Li2CO3–X2CO3}$ ($\ce{X: Na, K, Rb,}$ and $\ce{Cs}$) and $\ce{Na2CO3–Z2CO3}$ ($\ce{Z: K, Rb,}$ and $\ce{Cs}$) were measured using an ac two-probe technique and electrochemical impedance spectroscopy. The electrical conductivities of the eutectic compositions of $\ce{(Li_{0.52}Na_{0.48})2CO3}$ and $\ce{(Li_{0.62}K_{0.38})2CO3}$ at $\pu{923K}$ were $2.06$ and $\pu{1.31Scm−1}$, respectively. The conductivity of molten $\ce{Li2CO3–X2CO3}$ ($\ce{X: Na, K, Rb,}$ and $\ce{Cs}$) and $\ce{Na2CO3–Z2CO3}$ ($\ce{Z: K, Rb,}$ and $\ce{Cs}$) decreases with an increase in the ionic radius of $\ce{X}$ or $\ce{Z}$. We have succeeded in correlating the equivalent conductivity of a binary carbonate mixture $\Lambda$, with the composition ($x_\mathrm{A}$ and $x_\mathrm{B}$), the equivalent conductivities of the pure components $\ce{A}$ and $\ce{B}$ ($\Lambda_\mathrm{A}$ and $\Lambda_\mathrm{B}$), and two parameters ($\lambda_\mathrm{A}$ and $\lambda_\mathrm{B}$) as $\Lambda = x^2_\mathrm{A}\Lambda_\mathrm{A} + x^2_\mathrm{B}\Lambda_\mathrm{B} + x_\mathrm{A}x_\mathrm{B}(\lambda_\mathrm{A}x_\mathrm{A} + \lambda_\mathrm{B}x_\mathrm{B})$. The pair of interaction parameters ($\lambda_\mathrm{A}$ and $\lambda_\mathrm{B}$) can be estimated for a binary system of molten carbonates using the relationship between the cationic radii and the equivalent conductivities of the pure carbonates.


The table 107 in page 85 of government technical report (Ref.3) gives some insight to the conductivity (equivalent conductance ($\Lambda$)  and specific conductance ($\kappa$)) of molten lithium carbonate (m.p.: $\pu{618 ^\circ C}$ or $\pu{891 K}$; eq. wt.: $\pu{36.95 g/eq.}$) in different temperatures together with density ($\rho$) and viscosity ($\eta$) at the same temperature:

$$
\begin{array}{c|ccc}
\text{Temperature in }\pu{ K}  &amp; \Lambda &amp; \kappa &amp; \rho &amp; \eta \\
\hline
1010 &amp; 82.88 &amp; 4.097 &amp; 1.8260 &amp; - \\
1020 &amp; 84.58 &amp; 4.172 &amp; 1.8222 &amp; - \\
1030 &amp; 86.31 &amp; 4.249 &amp; 1.8185 &amp; - \\
1040 &amp; 88.06 &amp; 4.326 &amp; 1.8148 &amp; - \\
1050 &amp; 89.83 &amp; 4.404 &amp; 1.8111 &amp; 4.64 \\
1060 &amp; 91.63 &amp; 4.483 &amp;  1.8073 &amp; 4.34 \\
1070 &amp; 93.46 &amp; 4.563 &amp;  1.8036 &amp; 4.01 \\
1080 &amp; 95.31 &amp; 4.644 &amp; 1.7999 &amp; 3.67 \\
1090 &amp; 97.19 &amp; 4.726 &amp;  1.7961 &amp; 3.36 \\
1100 &amp; 99.09 &amp; 4.808 &amp; 1.7924 &amp; 3.10 \\
1110 &amp; 101.02 &amp; 4.892 &amp; 1.7887 &amp; 2.91 \\
1120 &amp; 102.98 &amp; 4.976 &amp; 1.7850 &amp; 2.83 \\
\hline
\end{array}
$$

The tabulated values of specific conductance ($\kappa$) for molten $\ce{Li2CO3}$ in this table were calculated from the data of Ref.1, Using the following quadractic equation for specific conductance (the precision is $3.00 \times 10^{-4}\; (0.0066\%))$:

$$\kappa = 0.9877 - 1.3529 \times 10^{-3} T + 4.3873 \times 10^{-6} T^2 $$

The uncertainty of the specific conductance values is estimated to be about $1.5\%$. The ref.3 listed this as the best equation for temperature range $\pu{1018-1118 K}$. However, the ref.3 did not provide the relevant units for these calculations and, unfortunately, I do not have access to the Ref.1.

The Ref.3 also provided three other equations for their calculations (I mention this only for interesting viewers):

$$\rho = 2.2026 - 0.3729 \times 10^{-3} T$$
The ref.3 listed this as the best equation for temperature range $\pu{1011-1115 K}$ (The uncertainty of the values is estimated to be about $0.2\%$).

$$\eta = - 5259.12 + 14.8091 T - 1.38581 \times  10^{-2 }T^2 + 4.31294 \times  10^{-6} T^3$$
The ref.3 also listed this as the best equation for the temperature range $\pu{1046-1122 K}$ exracted from Ref.4 (The uncertainty of the values is estimated to be about $3.0\%$).

$$\Lambda = 754.5 e^{-\frac{4438}{RT}}$$
The ref.3 listed this as the best equation for equivalent conductance (The uncertainty of the values is estimated to be about $0.15\%$). Here, the units are given as $\pu{ohm-1 cm2 equiv-1}$. The equation is derived from Arrhenius type equation, $\Lambda = A_\Lambda e^{-\frac{-E_\Lambda}{RT}}$. For $\ce{Li2CO3}$, $A_\Lambda = \pu{754.5 ohm-1 cm2 equiv-1}$ and $E_\Lambda = \pu{4438 cal mol-1}$.

References:


George J. Janz, Max R. Lorenz, “Molten Carbonate Electrolytes: Physical Properties, Structure, and Mechanism of Electrical Conductance,” J. Electrochem. Soc. 1961, 108(11), 1052-1058 (doi: 10.1149/1.2427946).
Toshikatsu Kojimaa,b,z, Yoshinori Miyazakia, Katsuhiro Nomuraa,* and Kazumi Tanimoto, “Electrical Conductivity of Molten $\ce{Li2CO3–X2CO3}$ ($\ce{X: Na, K, Rb,}$ and $\ce{Cs}$) and $\ce{Na2CO3–Z2CO3}$ ($\ce{Z: K, Rb,}$ and $\ce{Cs}$),” J. Electrochem. Soc. 2007, 154(12), F222-F230 (doi: 10.1149/1.2789389).
G. J. Janz, F. W. Dampier, G. R. Lakshminarayanan, P. K. Lorenz, R. P. T. Tomkins, In Molten Salts: Volume 1, Electical Conductance, Density, and Viscosity Data; National Standard Reference Data Series: National Bureau of Standards 15, US Department of Commerce, National Bureau of Standards, US Government Printing Office: Washington DC, 1968.
George J. Janz, Fumihiko Saegusa, “Molten Carbonates as Electrolytes: Viscosity and Transport Properties,” J. Electrochem. Soc. 1963, 110(2), 452-456 (doi: 10.1149/1.2425785).