Hi there,
The smaller the capacitor value the lower the power dissipation in any one diode.
Here are some measurements using 1N4001 diodes in a bridge and a sine input with zero source resistance, and adjusting the peak of the sine for each measurement to achieve a 10v average dc output voltage into a 10 ohm load (1 amp average output current), with various capacitor values:
200uf, 533mw
1000uf, 657mw
2000uf, 714mw
4000uf, 756mw
This shows the average power PER diode (multiply times 4 for the entire bridge).
For example, with 1000uf cap and 1 amp output the power dissipated was 0.657 watts per diode.
With 2000uf cap and 1 amp output the power dissipated was 0.714 watts per diode.
Extrapolating and taking into account the ratio of device parameter to circuit parameter:
2000uf, 362mw
so that would mean at 20 amps we would see about 7.24 watts per diode, or about 30 watts for the entire bridge
with a 2000uf cap. With a 4000uf cap maybe around 32 watts.
That's a significant amount of power and yes requires a heat sink.