Thanks everyone, makes an awful lot more sense now, I thought that a hot start was where the engine hadn't been given enough time to cool, rather than a lack of power in the starting system.
Good that you have a clearer understanding, but keep in mind, whenever you are thinking of a turbine engine, airflow airflow airflow.....that's all they care about really, so it's not that the power in the starting system is low, it's that the low power results in lower airflow.