I'm not sure how much removing the side of a case really does for cooling. Ideally there should be an airflow where cool air comes in from the front/side and warm air exits out the rear. If components are overheating it would be best to tackle the problem than cover it up.
Recently I cleaned my case and all the dirt that had built up on the fan blades/casing. Several dust bunnies were evicted.
Next up was removing the CPU heatsink, removing all the dust from that, cleaning the base of it and cleaning the CPU core, reapplying the thermal paste and refitting.
Even scarier was removing my graphics card (even that is a real difficulty with that silly PCI-e catch, which is completely covered by the massive GPU air duct), removing the heatsink from that, cleaning the copper base, GPU core and memory chips and thermal pasting those. During the process of this I was able to fish out big wads of fluff from inside my GPU heatink that weren't visible from either the inlet or outlet and was generally blocking the airflow through the cooler. I was pleased to find and remove it!
Long story short, putting a desk fan by my computer wouldn't have helped, and all of my overheating components would also be adding to the ambient temperature through radiation and circulating airflow.
PC is much cooler and quieter now (I had forgotten that it was once fairly quiet) and the results are as follows:
CPU idle: 42c > 33c
CPU load: 82c > 55.5c
GPU* idle: 62c > 49c
GPU load: 77c > 58c
*I set GPU fan to stay at 30% fan speed on idle test and up to 50% during load test, I've seen some scary numbers when fan software failed to startup once
Also as someone said, beep codes are dependant on motherboard / bios manufacturer so check your manual, or google the BIOS make for error codes.