If I understand this right, the Batterisers are making the batteries get so hot you can't touch them?
How would the batteriser heat the batteries? I suspect something shorted out in those LED lights.
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Could also be a short in the batteriser.
But my guess is that these lights draw a current that is on the edge of what the batteriser can do, and the batteriser thus has (extra)poor efficiency, and high losses. Due to the nature of the led light it needs a contstant power, and thus the battery needs to deliver even more power just to overcome the losses in the batteriser. And of course the batteriser itself is producing heat due to the losses.
Also the the current drawn from the battery is pwm'd by the batteriser, which gives higher stresses on the ESR and therefore more selfheating of the battery.
It's just a thought, but I think it's an interesting case to test.