The 405 had perfectly adequate heat-sinking when used as an amplifier for reproducing speech or music. Even with full-power testing, the heat-sinks would run hot, but not excessively so. The amplifier consists of a 3W Class A amplifier for each channel, augmented by the current dampers, so even at idle the heatsinks would dissipate some 20 Watts so would be warm (50% theoretical efficiency of each Class A plus the dumpers' standing current). I have measured quite a few 405s, and never found them under-cooled.
As to the performance into 4 ohms, that was a limitation of the original 405, but largely solved with the 405.2, albeit it never liked nominally 4 ohm loudspeakers that in practice dropped to 2 ohms or below, but then nor did many other amplifiers of the era. It worked superbly with KEF 104.2 and 107s which were purely resistive 4 ohm loads. It was very well protected such that it would survive pretty much any abuse. For use with difficult loudspeakers, (particularly successful with Mission Argonauts), putting the two channels in parallel worked a treat, Quad making a conversion kit available.
S.