The term is thermal breaker, not thermostat. These are not very common these days.
There is a flat, self-resetting circuit breaker which is very common. Also, many packs these days have at least a thermistor to communicate the pack's internal temperature to the charging circuit, but there is no standard thermistor size or terminal connections for this.
All lithium packs, and many higher end NiMH packs, have "smart charging" boards on the battery itself. The exact functions vary.
Usually simple float-charged cordless phone batteries are just the cells with no circuit breaker or thermistor.