My take from 'his' response ... "In practice, achieving a net positive energy output from such a system is challenging." ... is that although not easy, it is indeed possible.
I appreciate that it sounds a little bit like using an electric motor to drive a generator, but there is external input in the form of heat.
The bit where my knowledge is lacking is whether or not it is possible to have a heat pump with the required temperature differential to run the engine and still run at the required efficiency. (ie, is that possible even if we ignore inefficencies such as heat loss and friction).
The carnot cycle can at best get to 40% due to laws of physics. Don't know about heat pumps and don't seem to be able to find out despite many hours on Google and even a chat with your 'friend'. I've seen claims up to 600% but 400% is quite commonly banded around. You only need 34% on the engine and 300% on the pump to get a net output.
So, now that I've invented the "energy for free" engine. Next step.....build one.

Banter aside, I'm pretty sure it's possible.