I would guess it is a resettable fuse, otherwise known as a PTC (Positive Temperature Coefficient thermistor). Probably a 5A 16V max type.
Something like the F5549CT-ND, RGEF500-2HFCT-ND, or MF-RHT500-2CT-ND would likely be a reasonable substitute.
It would be placed in series with the battery rather than in parallel, as a capacitor would be. If functioning properly, it would have a very low resistance in normal operation (well under 0.1 Ohms), but its resistance would increase dramatically (at least hundreds of Ohms) when an overcurrent event occurs. Once the overcurrent situation is corrected, it should drop back to milliohms, again once it cools down.