Yep, I see your point and if you look at the threads posted previously you will see that the whole debate centres upon whether pressure altitude or density altitude affects the performance.
As density altitude is DIRECTLY related to the temperature this is directly related to engine performance. As the temperature goes up, the efficiency of the turbine goes down due to lack of effective combustion chamber cooling. Therefore, as your post suggests temperature has a huge effect upon performance but the question is why? I have attempted to answer that. Hot and High is a killer for helo turbines as they are not equipped with the correct type of variable stator/rotor compressors that large bore, high bypass jets possess. Temp goes up, density alt goes up, air thins out, ecu temp goes up and performance goes ..... down!
The original 'myth' was that turbine power depended upon the density altitude, which, in my experience (3500Hrs+) is not a myth but true.
As to the limitations they are, obviously, different for each machine but the principal behind why is common to each aircraft.
Does that make sense?