With a more integrated system (e.g. all Tesla hardware involved or simply a charger that can communicate with the vehicle's software), sensors and software may

With a more integrated system (e.g. all Tesla hardware involved or simply a charger that can communicate with the vehicle's software), sensors and software may specify what it needs to be in order for charging to commence. Otherwise it's generally an optimization rather than a requirement. The optimal range will depend on the class of the charger (how fast it's able to charge as well as sensors and software), the vehicle in question (the physical batteries themselves as well as cooling/heating systems), and other physical factors. In general: the faster the hardware can physically charge the battery, the more important temperature becomes.