It's a bimetallic thermal breaker or switch. The significance is it has a much longer cycle life than your typical re-settable fuse. They are not used much for the planned charge termination, well they were in some poor designs but unless you are sure that's the termination method, I would double check that first.
Often they are more of a safeguard against damage for example running a tool full speed, slapping it into a rapid charger in a high temperature environment, or of course a fault in a cell(s) or the load short circuits.
An important question is what happened. Having one fail without some other fault will not cause it to char the wiring like that. Its failure is the result of some other fault.
This 7.2V/3.6V battery pack, is it one of the poor designs similar to that I've seen in old Black & Decker 2 speed cordless drills, where the Low speed just taps into half the cells in series, so any time it is used, it's unevenly draining the pack and contributing to cell damage if subsequently ran on high speed before recharging, but eventually contributing to damage even if only ran on high because the most used cells degraded in lifetime capacity sooner?
If the breaker is the only method of charge termination it is a reasonable choice, but since 45C is within a typical, acceptable NiCd charging temperature range, if it is used as a safeguard rather than charge termination, a little higher like at least 50C or 60C at most would be my pick.