If the heatsink is properly mounted and the fan running at any reasonable speed the CPU should not skyrocket to 75-80C as soon as you place a load on it. It's possible the CPU has gone bad but it acts like the heatsink is not properly contacting the CPU heat spreader. 1.38v also seems a little high for an FX-8320 default vcore.
Check the fan speed to see if it's changing with thermal load and that it is running at high rpm when the temps are climbing. You should be able to hear it speed up and it should be running at full speed which could be 4,000-5,000 rpm when the temps are above 50C. You might also want to see if you can touch the side of the HSF when under load to see if it is hot. Be careful not to burn your finger.
If the HSF is not hot but the CPU is then something is amiss in the mounting. When you remove the HSF you should have a very thin, even layer of TIM where the HSF contacts the CPU heat spreader. Ideally you should have bare spots where metal-to-metal contact of the CPU and HSF occur. If not then the HSF is not contacting the CPU heat spreader properly.
The stock cooler if properly mounted and fucntioning should prevent overheating unless your room temp is above 90F constantly or you have PC case airflow issues where the hot air is not being evacualted from the case and cool air allowed to enter. The OE fan should be running at high speed most of the time when under load as the 8-core CPUs produce a lot of heat.
As far as a good HSF there are many depending on your needs, desires and budget. The link below has an excellent database of HSF performance tested under proper lab conditons and methodology. For serious cooling I recommend the Xigmatek Aigir SD128264 but there are many options.
Building a reliable PC involves more than just assembling the parts. You need to be able to configure all of the BIOS settings appropriately. This can be quite involved and frustrating as it can require a lot of trial and error with stress testing. It is however often the only means to get a 100% reliable PC.