First of all you have not told us if you are using a stock Amd cooler provided with the cpu.
Or an after market cooling solution for the FX 8320 cpu you have.
I presume it is an after market cpu air cooler.
Depending on the brand and model number of the cpu cooler, with a decent sized case.
And also with chassis fans.
I would expect about 33c to 34c. since you mention no overclock has been applied to the FX 8320 cpu you have.
AMD stock cpu coolers run slightly higher 36c to 37c.
What profile do you have set for the fan speed of the cpu cooler.
And have you currently got cool and quiet enabled in the bios of your motherboard.
Extra case fans do help with cpu cooling, so if you have space fit some.
If you are unsure about the thermal paste application, and want the cpu to run a few degrees cooler.
Maybe if you have not already buy some better thermal compound such Artic silver 5.
Don`t forget though air coolers are greatly affected by the environment they are in Davout.
So if your room is warm it goes some way to adding a few degrees to what you see.
Adding on average about 2c to 3c.
If the system is suffering from restarting, it may be due to a slight lack in cpu core voltage.
Not all FX cpu require the same voltage.
All the settings are pre fixed in a way to the bios firmware cpu micro code.
Basically a list of codes that identify a cpu to the board, where the settings for voltage, and other parameters in a table of the bios are stored to, identify, and run the cpu.
However in some cases it`s not enough.
The remedy is to apply a slight bit more cpu core voltage to the cpu it`s self in some cases, to stabilize it when running.
About 0.250Mv or 0.500Mv to the cpu core.
The other reason why the system may attempt to shut down or restart, can be down to any thermal temperature triggers set in your bios on the motherboard, so you should check to see what the reset, or shutdown trigger point is set in your bios of the motherboard for the cpu heat in oC.
As it may be the cause to the restarts.
The cpu it`s self can reach about 69c without much of a problem, that would be considered hot if the cpu was under load.
Again depending on if it was a stock AMD cooler used. Or very low fan speed applied to the cooler.
But go ahead with applying a new layer of thermal compound to the cpu and cooler if you wish.
It does often knock a few degrees off the cpu if applied right and the paste is of good quality such as AS 5 mentioned.
Long with all the other things to consider and check in this post to you davout777.
Just keep it all in mind.