So the drop from 13% to 8% when you got back is result of battery cooling.
Its not probably battery cooling.
First of all, these days we can see this difference as a blue part of the SOC.
Other, when the battery is very very cold, lile -15C I had a drop of about 4% from the battery being cold.
If we have summer, there is mostly no drop at all for most people. For me in the very north part of the world I might see 1% drop if the car was outside during the night and we had a very cold summer night.
The difference in this case almost certainly comes from the BMS recalculating (measuring) the true SOC ny measuring the cell voltage.
The true SOC can not be measured during a charging session or during driving.
This is because the battery will show a higher voltage during charging and a lower voltage during driving compared to when the battery is at rest.
During drives and charges, the SOC is calculated by counting energy in- and out.
In a perfect world, with a perfect BMS calibration the estimated SOC matches the true SOC at any time.
In the example below we disregard the buffer to make it easier:
Having a 80 kWh capacity fully charged and using 40kWh during a drive means 40/80kWh used = 50%. So the estimated SOC will be 50%. After the car was parked the Bms measured the cell voltages either with the car awake or when sleeping. As the BMS estimation of the capacity is spot on, the estimated SOC matches the true SOC.
We will not se a change in SOC after the car was parked.
(Sleeping will have the HV battery didconnected so this will be better/more exact)
If we had a BMS that overestimated the capacity by 2.5% (true capacity 80 kWh but the estimated capacity was 82kWh), this will happen in the same drive:
Starting value is 100% SOC, used was 40kWh/82 kWh = 48.8%, so estimated SOC after the drive was 51.2%.
After thw car was parked and the SOC has updated it would be 40/80= 50% used, so 50% remaining.
The car would show 51.2% when parking and 50% adter the BMS has read the resl SOC and updated it.
These calculated/expected SOC can be seen with Scan My Tesla and we can also see it update the SOC.
We can also see the displayed SOC reducing or increasing after a drive when the SOC is updated.
I have a lot logged data which covers this.
One of the best examples was a complete 100-0% drive during one day, at the same time as my BMS was fairly off, underestimating the capacity with about 3kWh.
After a 240km drive I parked with 52% and about eight hours later I stsrted the return drive, then showing 54% SOC. The math from the updated SOC actually matched the true capacity measured on the total 100-0% drive.
I was able to calculate how much the BMS was off by using the updated numbers.
To do this, SMT or similar showing the SOC in decimals is needed, and a longer drive to actually ”force a difference” between estimated and real SOC.
You see the impact much more at low SOC, on my MS90D say below about 20% when I park after a long drive with battery fully up to temp. The upper end shift after charging may be more of an evidence of the BMS calibration adjusting from my experience.
I see the updated SOC to follow the same pattern both with charging and driving.
Charging:
The SOC overshoots the set charging target - capacity overestimated.
The SOC undershoots the set charging target - capacity underestimated
Driving:
The SOC adjust down after the car has been parked for a while - capacity overestimated
The SOC adjusts up after being parked- capacity underestimated.
Both these need a true SOC to begin with, like sleeping before the drive (or fully charged). A long drive with lot of charges and no sleep will most probably set the initial SOC value a little off, so in that case the up/down adjustments can not be taken as true for the capacity.