Discharge Characteristics of Lithium Ion Battery
2A isn't a trivial draw rate!

It's very possible that your battery pack's internal resistance is many times that. If your battery pack was getting noticably hot, then you probably spent more power heating up your batts than heating up the external "test" resistor.

Try with a 24ohm resistor &amp; a voltage meter. When the meter registers 9v, turn it off &amp; call that "discharged" if it lasts longer than an hour, then you were definitely wasting most of your power against the batteries' internal resistances.