Converting a Lithium Ion Model from a Foster Network to a Cauer Network
Foster and Cauer models are canonical models for arbitary impedance synthesizing. Those gentlemen were circuit theorists. They decomposed rational s-domain impedance and admittance functions to continued fractions and partial fractions which showed quite clearly the needed component values. 

Different decompositions of the same impedance or admittance function give different circuits.

The current source in the heat transfer diagram is the heating power, only resistors and capacitors belong to the impedance synthetizations that Cauer and Foster invented. 

I see you have thought that the voltage source in your battery model is somehow in the place of the heat current source. You have totally missed the point. The corresponding part for the current source is the series connection of Uoc and what's connected to the battery terminals They together is what's connected to the impedance circuit. Sorry.

You can transform the impedance circuit  Ro + Up1 + Up2 to Cauer's version but voltage source Uoc and the plain line from the minus of Uoc to minus output terminal without intermediate connections must stay intact. I guess the change is useless because the presented parts have a certain understandable meaning in the behaviour of the battery. Cauer's impedance circuit would be totally abstract.