Just had another quick look around and found this site which gives lots of info on batteries. Here is a quote from it.
As all drivers in cold countries know, a warm battery cranks the car engine better than a cold one. Cold temperature increases the internal resistance and lowers the capacity.
Here is the site:-
http://batteryuniversity.com/learn/article/discharging_at_high_and_low_temperatures
yes, your battery internal resistance is higher at 0 deg C than at 20 degrees C but that is due to the construction of Lithium ion cells.
Your cells are optimised to functioning temperature at 25 degree C. That is, the internal resistance is higher too cold or too hot, lowest between 20 - 40 deg C, then rises again.
Your battery will heat up when you are using it, but you get quickly to an equilibrium, somewhere about 5-10 degrees higher than ambient temperature. This is seen with a 10AH battery, less with greater capacity like 13AH or 17AH battery. The effect of temperature is nevertheless small to insignificant compared to the Peukert effect due to the high discharge current.
Read the datasheet of the Samsung 18650 29E, probably the most popular cell on e-bikes.
https://eu.nkon.nl/sk/k/29E.pdf
Page 4 and page 5 explain the effect of temperature on the cell.
Page 6 explains also the effect of high discharge current on the amount of energy you get, 1C, 2C and 3C: 0.2C: 100%, 1C: 97%, 2C: 95%, 3C: 92%, the reduction is dissipated as heat due to increased internal resistance.
In order to understand why cell performance decreases with discharge current, you need to go back to the
Arrhenius Law.