Funny that you mention it, as I remember performing high school physics experiments with discharging a battery (not a capacitor), and due to heating there was very significant deviation from exponential decay - as battery discharges power, it heats up, and it changes it resistance. That's more 10% kind of error than order of magnitude kind of error. (with a capacitor heating will more likely occur inside the load than inside the capacitor, but you might get similar effect)

And of course properties near complete discharge will be very different, what should be very clear on a log-log plot.