Badaphooko01 :
overheating was due to cpu cooler not being fully secured. Bad quality control.
TL;DR= This PC stock (with proper cpu cooler mounting/thermal paste/dust removed) is sufficient. It runs the fans at base rpm until the cpu core temps reach 80C, then begins ramping up the fan speed. Mine never went over the 80-85C under 100% load Prime95, according to multiple cpu temp monitor programs. The fan curve doesn't seem to be controllable aside from setting base fan speed 1-7 in BIOS. =TL;DR
I own the same HP 8200 Elite sff. i5 2400 8gb ram (an incredible value for $100 + ram(at the time), usb wifi, usb bluetooth, low profile GPU, and fans upgrade cost). Mine according to HWMonitor and other cpu temp programs never goes above ~80C under 100% stress with Prime95. Idles around 27-35C. Same stock cooler setup as the picture Lutfij posted. It's an interesting proprietary design, bringing cold outside-of-case air right onto the weak looking (compared to full-size aftermarket) cpu cooler.
I also replaced both cpu and psu fans with Arctic f9 pwm pst. The original stock fans were worn out and crunchy sounding even after cleaning. Much much quieter, smoother fans with the f9. I think the stock fan may have spun faster too though and had a different blade design, hard to tell as there is no way to view fan active RPM/percentages with any program I've tried; it's locked. Of course, being 92mm fan it does make some light, soft, smooth hum in a very quiet room at base speed and can be heard from a distance when full speed... like any fan. It's still a soft, smooth hum though.
This 8200 elite sff motherboard has a proprietary pwm control based on cpu core temps and has locked "fan curve" that usually is fully controllable as with retail motherboards BIOS/UEFI. One can only set the base fan speed on this motherboard, which you can set in the bios (press ESC at start up, computer setup(F10), under Power tab select Thermal, the Fan Idle Mode can select 1-7 level (its shown in ****** asterisks), 1 being the slowest rpm. (F10) to accept, Under File tab save and exit, it'll ramp the fan speed after a reboot.) So if you want to hear how load it can be set it to max and it'll run max speed all the time. So, if you know you'll be stressing it you can pre set it to full fan speed, it does seem to keep the temps from rising as fast as well as keep the temp in the 70-77C under full load. I have mine set to slowest rpm as the temps are good and the mobo will slowly increase fan speeds with cpu core temps reach 80C.
I have been considering and looking into aftermarket cpu coolers, but am weary the mounting holes are proprietary as well; I'm not sure. The size constraints etc. There is a 3rd fan connection and seems to run the fan at max I believe constant. I'll take some measurements and see if any cooler might match up. Besides, my temps are just dandy in stock config. Why mess with it? Glad you found the problem.