if the temperature difference between hot and cold side is too large one might need multiple heat pipes in series each operating at their own temperature. The hot side heat pipe might only act as a heat pipe as it nears its operating temperature, i.e. it might be solid during travel, then melt during the first phase of entry, and only reach both vapour and liquid phase -thus enabling it to work as a heat pipe- during the hottest part of re-entry
alternative idea:
the solid aborbs heat (cools the shield) to melt, then absorbs heat to warm up and boil, and the boiling gas is used as retro-firing rockets, any decrease in momentum due to the retro-rockets is less future heat absorbed (since the craft is slowing down faster)
think controlled steam explosion
This is much easier said than done. If such a conversion were simple, we would not use turbines in nuclear or geothermal plants. You might be interested in looking into thermocouples [1], however.
Also of note, any such conversion must by nature exploit an energy gradient, which means any energy spent redirecting particles in such a manner would heat up the interior of the spacecraft by an equivalent amount.
[1] https://en.wikipedia.org/wiki/Thermocouple