I think your diode fell victim to thermal runaway. As the diode warms up, the Vf for a given current falls, so more current flows, making it even hotter, etc. until it burns up.
That would explain why the diode kept heating up after you stopped charging. The Vf had become smaller than the voltage that the capacitor was charged up to, so it continued to discharge.
Generally, connecting a diode directly across a low-impedance voltage source (which a supercapacitor most certainly is) is a Really Bad Idea.
Putting a current limiting resistor in series with each group of diodes. Choose the value so that the voltage drop across it at 1A, plus the Vf of the diode at 1A, is still within the voltage limit of the capacitor.