Linus Tech Tips did some
testing a while back with different fan configurations and they found that the difference between having 1 front intake fan and 1 rear exhaust fan and having just the intake fan resulted in a difference of 7 degrees C on the CPU and 1 degree C on the GPU while running a stress test. That's a significant difference but the system wasn't running dangerously hot or anything without an exhaust fan.
If it was me I'd just put the cover back on the case (having internals more exposed is probably more likely to result in something breaking than the extra heat) and get another case fan. They cost like $10 shipped and are pretty easy to install.
Water cooling systems are more like a hobby project to me than something you do for the sake of practicality or economy. My understanding is that properly set up air-cooled systems offer similar or superior performance (both in terms of thermals and noise) with much less risk of something going horribly wrong. The main advantage of water cooling is that it can give the inside of your case a cleaner look.