Beware, I know nothing of what you write, but can you attach some sort of sub-woofer-type power sink? I know nothing... but SFAIK a sub woofer is put in series with speakers in order to protect them from blowing. A silent, but high impedance power-sink might have the desired effect of generating the heat outside the amp.
Otherwise, what about installing a fan, or drilling larger ventilation holes in the box. Clearly the amp is no use for your purposes, so you might as well either (1) sell it, or (2) bin it, or (3) attempt to fix it.
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