To be fair, the use of chickens in this project would have been perfectly reasonable. The chickens simply act as a heat source to protect the mechanism, they do not power it. An engineer today would likely make use of the thermoelectric effect to generate heat through electricity. Why use chickens instead? A few reasons might be: Materials were not as advanced then, so an electric mechanism would have been less reliable and more prone to failure; an electric mechanism would require its own power source, which could create its own problems; an electric solution could generate noise or otherwise be observable; a chicken is sufficient.

Why would chickens be sufficient? In winter the temperature a small distance underground is reliably stable, and warmer than temperature above ground. They likely would have been able to get a good idea of what the operating temperature would be and what they would need to offset it. Luckily, the heat output of a chicken is also reliably measured/estimated.

On the other hand, the whole notion of creating a nuclear mine is completely bad. No way to justify that.