Project feasibility and cost

Sacman:
Using power monitoring equipment , we were able to prove that it was far more energy efficient for them to remain on.

I'm surprised to find that - I'd have thought that the electrical energy requirements were directly proportional to heat loss which (other things remaining constant) would be driven by temperature difference and time. In other words I'd expect that an extruder which was allowed to cool and them reheated would lose less heat than one which was kept hot continuously, and so would use less electricity. Is there some other factor here which makes the reheating process particularly inefficient?