The surviving terranauts manage to outrun the ultimate nuclear blast because the ship’s hull can convert heat into energy. Can you convert heat into energy?
No – that’s the whole “2nd law of thermodynamics” thing. You can turn a heat gradient into energy (hot air inside a piston in an engine pushes against cold air outside to move a car), but grabbing heat out of the surrounding environment to move a ship is straight-up magic.
This is not correct. Heat can be converted into work, that’s how steam engines and nuclear reactors and Stirling engines operate, to list just a few examples. His explanation of how internal combustion works is bizarre too — “inside a piston?” Pushing against cold air? No, the expansion of combustion gases push against the piston, it doesn’t much matter what temperature it is outside the engine (as long as it’s not as hot as the ignited fuel-oxidizer mixture.)
It is true that the ship would have to be hotter or cooler than the surrounding medium for any heat exchange to take place, but he really doesn’t explain this point well at all.