More to the point - what's the pressure in the case? Do you - by any chance - have more exhaust fans than intake fans? I suspect that beefing up the PSU fan could make your problem worse.
My guess is that your exhaust is already more than your air intake. What that means is that you're trying to shove out more air than is coming in - in other words you're trying to create a vacuum in there. Now you won't create a vacuum because (1) your case isn't airtight (2) if the negative pressure is severe enough then the air will flow in through the path of least resistance, which may even be reversing through a (weak) exhaust fan.
I had a similar experience. The 2 intake fans and the case exhaust fan are all thermistor controlled. The intake thermistors were always cooler than the exhaust thermistor and I was generating negative pressure such that air was flowing IN through my VGA Silencer exhaust .
Low pressure is bad - cooling in forced convection has a relation to the density of the cooling fluid - in our case air.
My load temps dropped when I reduced the rpms of the rear exhaust fan to the point that I was no longer seeing inflow of air through the Silencer - in other words pressure was give or take equalised.