A hot battery should not be rapidly charged. The i3's logic won't let it happen. Charging does create heat, and the faster and longer you do that, the more heat is generated. Rapid or sustained high charge and discharge rates warms the battery pack.
Even if the CCS unit is in the high 90% efficiency range, if it has 50Kw output, it will be making some serious heat! They, like the internal components in the car, must manage their temperature. Assuming the CCS unit's cooling fans and filters are not compromised, depending on how hot it is, it just may end up overheating and reducing its output. THrow a solar load on it, that can just complicate the issue. Whether the thing had just finished a charging cycle on someone else when you arrive, could be a factor verses it sitting there idle for hours.
Much higher current rates are coming, and that will just make it even harder. Newer battery tech seems to have less internal resistance, so that bodes well since it won't create as much heat. THe future looks more promising when it all starts to come together. Ideally, you'd draw power from the electric roadway, and never need to stop and recharge the vehicle. That too, may happen outside of test tracks.
2011 535i x-drive GT, 2014 i3 BEV
Soon (hopefully!) A 2021 X5 45e will replace the above