The processor won't burn out it will just shut down the computer before it is damaged. Still it isn't a good practice for a processor to shut down a computer constantly due to overheating.
Are you using your Motherboard's BIOS Fan settings or a Fan control software like MSI Afterburner or Radeon Wattman?
When did this behavior start to occur?
The same day you installed your processor or just recently after either updating the AMD Driver or Windows Update or MSI software?
EDIT: As a temporarily work around you can always disable "Sleep" and "Hybrid Sleep" in Windows Power Plans until you find a permanent fix.
To make sure your Windows OS is not corrupted or missing important core files run in a elevated Command Prompt or Powershell - SFC /scannow.
Also in Windows Power Plan make sure you have "Fast Startup" unchecked:
This may cause BSODs and other problems if enabled. Same thing in BIOS Setting. Disable Fast Start.