Overheated CPU
Overheating in CPUs is mostly caused by handling during shipment. The heat sink probably fell off. This is often left unchecked until such time that the CPU starts to overheat because people seldom check items that reach them from shipping, What they usually do is just run a virus scan then back up the system and open the PC case to look inside, but with no particular concern whatsoever with the heat sink.
If you suddenly smell burning while working on your PC, you should unplug the unit immediately. Don’t look around anymore for the source of burning wherever it may come from. Just disconnect it at once. Next thing you should do is call the manufacturer if the machine is still under purchase warranty.