After a day of pondering, I came up with this:
Its a semi closed loop system. The amount of exhaust effects the amount of intake. How do we improve the efficiency of this system, to get more power? Find the current worst bottle neck and eliminate it. The goal is a balanced system.
If the intake is a drinking straw, it doesn't matter what size turbo is there, you can only move so much air at a given pressure. Increase the size of the straw and a point is reached where that no longer is the bottle neck in the system. Keep increasing the intake flow capabilities and you get no more results because something else is now the restriction. Perhaps the next bottleneck is the cam dynamics, and the cam is not suited to a performance turbo motor. Install a cam better suited to a turbo motor, flow goes up and now the bottleneck is the exhaust. Its not converting enough exhaust energy to intake charge. Port the exhaust to allow the exhaust turbine to better use the exhaust energy, and you will see improvement until the turbine is the new source of restriction to the new flow levels of the rest of the system. It can't handle the flow the engine is capable of, and instead of converting it to intake energy, it maxes out and heat is the result. Install bigger/higher flowing turbine and the restriction is now moved to the compressor. Up the size of the compressor to match the turbine, and you will now see the power gains. Balance.
If the components are sized correctly to each other, the system should be working in balance, at a new hp level. There will always still be a small bottleneck somewhere. Want more power? you need to adjust the whole system to a higher balance point.
I realize I never included heat, at least not directly. Too much heat is evident in a system that is not in balance. Something along the way is causing resistance. Heat is a product of inefficiency. Ideally all the exhaust energy directly equates to intake charge. This is not true and the difference is heat. Heat should not be a factor in a system designed in a balanced and efficient manner. Heat is an indicator of inefficiency. You can't get away from the heat that is created when you compress a gas, That is physics. You can however reduce any additional heat applied to the air by the inefficiencies of the system by achieving balance.
What are intercoolers for? To reduce the heat you can't get away from. It is not for reducing the heat created by mismatched components.
This requires looking at each part separately, and seeing if it is the current bottleneck in the system as a whole.
If volume is the sole dictator of performance, all 2.3L turbo engines would make the exact same power at the exact same boost levels.
But this is not the case, is it. Ford 2.3 turbo guys struggle to get "big numbers". 2.0 mitsu engines throw down big numbers.
1.6L hondas, big numbers.
Ergo, volume cannot be considered static.
The volume IS static. The volumetric efficiency varies. Those motors all have different stroke/bore ratio, head configuration, rotating assembly mass, compression ratio, valve size, cooling, oiling, etc.......All of these factors play into the VE of the engine and why those engines do or do not make power at a given displacement.