It is no where as simple as thinking "we need to pull the hot air out, not push cool air in."
The simple truth is you can only pull the same amount of air out of the case as in going into the case... and you cannot push more air into the case than is coming out of the case.
There is airflow
and there is airblow
What usually happens is lots of airblow
and heat air mixing with cool air.
What we want is guided airflow
that flows the heated air out of case without it mixing with cool air.
All of the variables; components, cables, airflow and currents from GPU and CPU coolers as well as by case fans pushing air in and pulling air out, turbulence created by air flowing around HDD cage, cables, compoents, etc. make it extremely hard if not impossible to predict what the airflow will do and how well the heated air is kept separate from cool air.
Airflow is a very fickled witch and often the airflow we think will happen is not what does happen. Every case (no pun) / system has some differences and those will more often than not change the airflow... sometimes only slightly, sometimes dramatically.
And that's why no matter how many tests and results we have we still need to test the system in front of use to see what the best combination is.
In most cases (pun intended) we test until we are satisfied with our temperatures and stop. It is just too time consuming to keep going...
I've posted this basic tutorial many times:Warning: Spoiler! (Click to show)
There is much more to cooling than good cases and good CPU / GPU coolers. Modern GPU's make more heat than CPU... and getting that heat out of the case can be a challenge.
Setting up the case to cool properly is the hardest and most time consuming part of a build... And the most neglected by most builders.
Cases, especially those with filters, usually benefit from fans with higher static pressure ratings than stock fans... "cooler" fans instead of "case" fans.
Intakes are typically more restricted than exhaust; air filter, more restrictive grill, HDD cage, etc.
I prefer more intake than exhaust. And don't confuse number of fans with amount of airflow... or airflow
is flowing cool air from intake to component and flowing hot air from component out of case without the hot air mixing with the cool air.
is lots of fans blowing air with some of hot air from components mixing with cool air making it warmer resulting in warm air not cooling components as well as the cool air will.
Putting fans in case as intake and/or exhaust is only the first step. These fans only move air in and out of case.
This does not mean heated air is not mixing with cool air.
Nor does it mean cool air is going to where it is needed.
Getting the air to flow inside of case properly is even more important. We still need to manage where the air flows inside the case. We can do this several ways; deflectors, cooler intake fans, exhaust fans, removing vent grills, using fans with higher pressure/airflow, building ducts to or from CPU/GPU cooler, etc.
Using a remote temperature sensor to monitor what air temps are is the key to finding out where the cool air is flowing and knowing heated air is not mixing into it. By monitoring this we can than make changes to get airflow the way we want it.
I monitor the temps with a cheap indoor/outdoor wired remote or terrarium digital thermometer. Twist a piece of stiff insulated wire into the last 8" of sensor lead so you can bend it to position sensor where you want it... like 40mm in front of your GPU cooler/radiator intake.. to see what the air temp going into CPU / GPU cooler is compared to room temp. The closer it is to room temp the better.. Shouldn't be more 5c maximum, 2-3c is what I usually end up with after 30 minutes full load on both CPU and GPU.
Warning: Spoiler! (Click to show)
Bit-tech did a cooling test on a Define R3 using 1 to 6 fans. Problems are they don't make it clear which were intake and exhaust... and they may many assumptions without verifying them.