The internal resistance of the battery actually increases with the temperature increase.
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The power that can be drawn from the battery is linked to the speed of chemical reaction that produces current. I am pretty sure that for all batteries, including Li Ion, the speed of chemical reaction increases, up to a certain point, with the increase of the temperature. Another factor is that internal resistance also increases with the increase in temperature, so at certain point one negates another, so the power out of the battery increases with the temperature up to a given value of temperature.
I did not spend time reviewing the API data, but you might want to take another look at the data: either your recollection is off, or may be the data are not accurate.
The modeling of the battery under various conditions, including ambient temperature, state of charge, age *and* prior loading cycle, I believe, is a very complex task. I've used google search and skimmed through several scientific articles. It seems that there are various models available, each of them successful in modeling of real life behavior of the batteries to the various degree.