Technically yes. In your question there is a lot missing. First Battery is a power source like any other source unless you place a load no current flows. So it’s only the load that determines the current draw. Now batteries are rated in “C” in time to discharge at some current load. So they use this to rate current max. and current max may be destruction or over heating or made up “LOL”. BUT it is caused by the "ri" internal resistance of the battery.
Bottom line to low “C” overheat to high ”C” only weight an size.

Rich