I bet if thicker aluminum was used and it was curved to match battery shape and then heat sink paste was used in the middle to help with thermal “connectivity”, that cooling could be improved.
Could get mighty messy, especially if the batteries were to be installed in another enclosure after charging.
Probably get just as much improvement by dropping the batteries in a good airflow.
Or in mineral oil.
You’d only get increased heat flow to the air by conduction if the outer diameter of the aluminium layer was substantially
larger than the battery/cell diameter - this would mean more surface area to transfer heat to the air.
Think in terms of thermal resistance - aluminium has basically no thermal resistance compared to the that of transfering
the heat from solid to air (in still air conditions), so the aluminium foil has no noticeable effect. The limiting factor is
that still air is an extremely poor conductor of heat.
However as others have pointed out the thermal radiation will depend critically on the nature of the surface - painting the
battery black (well with a paint that is “black” in infra-red spectrum) will maximize radiated heat. Aluminium foil that is
black on the outside will clearly have an effect.
Plain aluminium probably has very low emissivity and wrapping a battery with it would substantially decrease radiation losses.
However without knowing how much heat is lost by conduction to the air (compared to radiated into the surroundings), the
magnitude of the total effects is guesswork.
One thing is sure though, forced air cooling works really well and is simple and straightforward.