Changes in battery temperature most definately impact the SOC.
Lithium batteries is very, very temperature stable for cell voltage, at no load (OCV or low load).
(I performed a test in extreme cold with panasonic NCA cells: Cell voltage in -25C)
The BMS measures the OCV and this is the way the BMS finds the true SOC.
Any time your car displays a lower SOC due to a cold battery the BMS is able to measure the real SOC.
That is, if you have 70% SOC and leave the car in very cold winter the BMS will know the ”real” SOC from measuring the OCV which will say 70% even if the batteries is cold soaked to -15C.
But to compensate for the losses for heating the battery etc, the car will show you a lower SOC than the real SOC.
I have seen this hundreds of times, using Scan My Tesla and a tablet in front of the steering wheel showing all BMS-data.
This can since a time also be seen in the Tesla app and for example teslafi, both the ”displayed ”cold” SOC and the real SOC can be seen.
Today my cell temp is 18C and there is no reduced display of the SOC.
We probably would need <15C to see 1% reduced SOC from the cell temp.
I have data from the car beeing out in a very cold environment over one week and when the cell temp was -15C, the displayed SOC was 4-5% lower than the ”real SOC” red from the BMS.
A temp decrease after driving or charging do not change the displayed SOC unless the cell temp goes quite low.
For the 5% loss, it probably is the cooling circuit and also the cell balancing. Tesla burns of the high cells, which after a complete balancing ends up in a lower SOC than after the charging.
Also, there have been numerous posts of late in which, after charging has completed, the SOC changes more than a little bit, up or down.
SOC change after a charge mostly comes from that when the BMS has for example a overestimation of the battery capacity, the calculated value ”to charge complete” is to much energy.
When charging or driving no good readings of the true SOC can take place, so the car estimates the energy needed to hit the set SOC number.
A overestimated capacity will mean to much energy is added, and after the charge is finished the BMS can measure the cell voltage and then the SOC is updated. In the case of overestimation the SOC will be higher than the set value.
Overestimation will also cause the SOC to seem to drop after a longer drive, when the real SOC is measured the real SOC will be lower than the calculated duribg the drive so the SOC will drop from the moment of parking to sbout 20-30 min to one-two hours.
Underedtimation will cause the opposite for charging and driving.