It has a fan because the parts aren't specified to be able to run in the kind of temperatures you get without some forced airflow. But I guess it depends on your case configuration. Stock Antec 300 may actually help the power supply out because it must be mounted at the bottom with the fan opening on top, and the case has negative pressure with 120mm and 140mm fans on back and back top, meaning those should draw air through the back of the power supply up through the top (as well as from the front and side). Of course, that's still nothing as good as having forced airflow from the power supply fan that it was designed to run with.
However, some rather ordinary power supplies seem to run okay fanless until about 20% load or so (which is where you're at with E3400 and GT 640) like current Corsair GS or so, but those are a little better than CX.
Just consider that you've been stressing a mediocre-quality power supply hard the last couple of years. Haswell or Broadwell may not mean more power consumption on the CPU side, especially if you don't overclock and especially if you get a dual core, but larger upgrades on the GPU side may not be the same. I wouldn't trust expensive new hardware to a compromised power supply, and I wouldn't be surprised about impending failures, even with the modest power draws you're seeing, considering the quality and position of some of the capacitors and lack of airflow to them.
Originally Posted by shilka
Unless it has no OTP it would just shut off
Doesn't have OTP. Most cheaper power supplies don't. And if the fan was being too loud, that was probably from the thermistor for the fan control essentially giving bad readings.