I have maintained PT6 for over 40 years and have started them with varying states of battery charge and have never had an overtemp on start.
If the battery is too weak it will not generally spin it above 10-12% and should be enough warning to abandon there and then. If not then a hot start and CT wheel burning is assured, not to mention the NGV.
I have on my computer very descriptive pics of that and will try and post for the benifit of those who have not seen the damage which can be done with hot starts.