No takers ?

Anyway, lets do some maths:

Specific heat of a Li - ion battery is roughly 1000J/kg*K. In other words to raise the temperature of 1kg battery 1 Kelvin we need to apply 1000 Joules of energy.

Lets assume we have 90kg battery at 25*C temperature. If we take this battery to an environment which is as cold as -177*C i.e. temp. diff. of 202*C. Therefore to reach thermal equilibrium, 18.18MJ of energy must flow from the battery to the environment until thermal equilibrium is reached. Assuming ballpark efficiency of 40% for a good stirling engine we have 7.2 MJ energy available for recovery.

Assuming a normal energy density of 0.90MJ/kg this approach gives us extra 0.09 MJ/kg

10% increase already !!

edit: 10% is without taking into account the self heating of the battery during charge and discharge which work to our advantage as well.