Why Does an EV Charge Slowly at a Public Fast-Charging Station?

I’ve had a few trips where my electric car charged much more slowly at a public fast charger than I expected, even though the station was advertised at a high kilowatt rating. The car’s battery wasn’t full, but the speed still varied a lot between stops.

How much of that difference comes from battery temperature, the car’s own charging limit, or sharing power with another vehicle? I’m trying to understand what information is useful to check before assuming the charger is faulty.