Your fan might be clogged with dust. I periodically charge up my air compressor to about 80 PSI and use a dust wand to blow the dust out of my power supply / heatsinks.
First thing I'd check is if there is any software running the cpu at a high % all the time. Does it happen as soon as you turn the computer on or after the OS starts, etc. Definitely check if there's a BIOS firmware update available. I'd say probably the GPU fans clogged with dust, that can be loud. Check that, the PSU and the CPU fans. I opened my case while it was running and was able to tell directly where it was coming from. If cleaning with an air compressor, I'd make sure to have a moisture trap on it. You can pick up an inline one for cheap. Also, use something to keep your fans from spinning while you dust it out if you're hitting it with high psi.
You want to run the fan as fast as possible, it is much easier to replace a fan than a new expensive GPU or CPU
Clean fans of dust, re-apply thermal paste. Done. Running computer open is a bad idea because it means there is no air flow (normally from front to back). BIOS updates are for almost always for compatibility fixes, not temperature related.
You can pop the case off to see what's making the noise (don't touch anything in the case) and then turn it off and dust. No one said run the case off all day. I didn't have to take my cpu fan off, but if you do, you have to clean old thermal paste off (91% isopropyl alcohol) and re-apply. Pop your cpu out and clean it off the board. I never took a fan off the GPU, and in my case that was what was causing the ruckus.
I have heard this before, but it assumes that the computer already has some powerful fans to produce good airflow through the case. There are tools to monitor the CPU temperature. I'd measure and see if that's really the case. Another option is liquid cooling.
It is suppose to create a draft system of positive and negative forces to remove the heat. So say the fans pull in from the front and push out the back. You have a good cycle with good induction. You open up the side panel, it pushes air out the side and sucks in from the side, you never had anything really go against you board. Liquid cooling is kinda of good for overclocking, and kinda bad. There is no cpu fan so unless your case fans are great i would lean away from it. I would never really get liquid cooling for anything myself. They never shown a improvement over a large air cooled heatsink like a cooler master evo. Most cases won't support such a large heat sink but that still not the deal with this guy. He never said what fan it is. Dell is pretty proprietary, meaning you have to buy there stuff or know how to wire. Fans should be excluded in that adventure but you never know with them.
I've done measurements many years ago. Yes, CPU/GPU ran slightly cooler with an open case but hard drives (this was pre SSD) ran very hot. Had one fan taking the air out. Don't forget, if you give air lots of unfiltered access points, there's also more dust accumulation.