I'm not sure that's accurate. Not much was explained about the "final shape" he wants to help the universe achieve, so I can't say if it really is about heat death. It should be noted that he thinks that the universe will simply end if this final shape is not achieved.
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The Heat Death isn't really an end. The Universe still exists, but no energy is left. It is simply dark stillness for eternity. "Final Shape" is a fitting term.