Well I hope you know this thing is an excellent heater, do you? So it generates heat and even if you take it out from the case it will accumulate it in the room. This is the nature of the beast, it is all about thermodynamics. There is no way around it.
This, sort of. Most discussions of cooling are referring to lowering the temperature at the points of measurement (at the CPU, at the DIMMs, etc.). Increasing airflow inside the case can lower those temperatures, but the amount of heat being generated is not changing - you're just shifting it from inside the case to outside (which is good for prolonging the life of your computer, but raises the ambient temperature in the surrounding room).
To decrease the amount of heat generated, you have a few possibiliities, most of which boil down to the same thing - remove any unnecessary items from the case. If it's a simple SMB server, remove as much RAM as you can tolerate. Likewise, if it's a dual-CPU system that's only going to manage disk storage, I'd remove one of the CPUs and maybe replace the remaining one using a compatible chip with a lower TDP. Not using WiFi/Bluetooth? Remove those adapters. Remove any non-essential PCIe cards. Replace the GPU with the least powerful one that will still do the job (e.g. NVIDIA GT710). Non-essential spinning hard drives should be removed or replaced with SSDs.
(You can also try undervolting the GPU and/or CPU, but that's a tricky operation that's probably not worth your time.)
Every chip and motor inside the case generates heat; while the CPU/GPU/Northbridge are the furnaces, even the little chips add to the total. If you want to lower the heat output, you need to lower the chip/motor count, and/or lower the power consumption of the remaining chips. Even then, you're not likely to lower the ambient temperature more than a few degrees.
Good luck.