The log(conductivity) vs 1000/T plot gives a positive slope which is not reported any literature
You might find the ionic conductivity of some types polymer electrolytes to decrease when we increase the temperature in some range in the following paper.
J. Electrochem. Soc. 2015 vol. 162 no. 14 A2551-A2566
Review—On Order and Disorder in Polymer Electrolytes
But the conductivity of so many polymer electrolytes can be explained by an Arrhenius plot(or non-Arrhenius conductivities).
Arrhenius and non-Arrhenius conductivities in intercalated polymer electrolytes
The Journal of Chemical Physics 109(18):8109-8117
It is possible. Conductivity is the product of number density of mobile ions, charge and mobility of the carriers. Number density of charge carriers can drop with temperature and ionic mobility can increase with temperature, The product of these two parameters can also decrease. Hence it is possible. Other factors mentioned above are also true.
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