Firstly
there is no OU from heat. Energy from heat is a Maxwell demon, i.e. the transformation of heat energy from a single thermal bath into useful energy (mechanical, electrical...). This hypothetical process obeys the energy conservation. It's a way to get useful energy endlessly, but it's not OU.
Secondly a definition of OU that would depend on our knowledge of a system, as this proposed by Physicsprof, is
not a scientific definition. For this one who would ignore where the energy comes from, it would be OU and for the other one who knows, it wouldn't be OU?!
There is a terrible lack of intellectual requirement in such inconsistent and unprecise definitions.
Once again, in order to evacuate the viewpoint of the observer from the OU definition, we must leave our intuitive but misleading sense and define OU relatively to a well described system.
If a system showing more ouput energy than input, is given without the extra-energy source or without taking into account the energy flux at the interface between inside and outside (for any reason, including the ignorance that the system is not really closed), then we have OU.
If it is defined including the energy source, either inside, or outside but with consideration of the energy flux crossing the interface, then we have not OU.
Of course once the source is known, it's natural to take it into account and thus, to no more consider that there is OU. But this is not the point for a definition that must apply in any circumstances independently of the observer.