Drawing more continuous current would build up heat quicker than it could be dissipated, with some sort of results, most of which are not nice. But, you could draw more current that the maximum if it was in pulses, allowing the battery time to cool between pulses. This is starting to get into engineering which is beyond the scope of this article. Call me if you would like further information. A rating for a battery also will specify the temperature at which the ratings were determined.
Higher temperatures mean quicker chemical reactions.
Some batteries are more temperature sensitive than others. We're going to knock off here. Next issue we'll pick up with rechargeable batteries. Be patient, and don't get your liver in a quiver. The information in this part is necessary to understanding much of what we will cover on rechargeable batteries.