Fatguy 46 may be on to something. The fact that fps drops as you start to play may be a heat related issue. That could be thermal paste on the heat sink. It could also be that your cooling system isn't keeping pace. For example on an air cooled system you want fan speeds to increase as you play a complex game.
The thermal paste's job is to help the cpu transfer heat to the cooling system. In store bought computers the thermal paste is applied by a machine to the bottom of the heat sink (the part that directly touches the cpu) and so when it's all tightened down it should work OK.
I have seen commercial builds where the whole cooling unit is dropping off because the brackets that hold it are cheap plastic. The grapahics card and the cooling system are the two known things that are most frequently damaged in shipping.
When my computer began overheating and shutting down, I saw that the plastic bracket that held it had broken. I bought an aftermarket fan with a really nice metal bracket. When it happened to my friend, he took some plastic tie wraps and held the fan down that way. That's really living on the edge. He makes a great salary but is stunningly cheap. I admire him for being so cheap. I mean, an inexpensive replacement fan would have set him back $35. But his repair lasted for years. Myself, once I had replaced the fan and mounting bracket on the computer I realized that I could pull out and replace just about anything in there. And that's when I migrated from buying store bought to do-it-yourself.
The cooling unit should feel solidly seated at a minimum.
If the thought of opening up a computer is scary (it was for me, I got through much of my adult life carting computers to shops for repairs), watch some videos. I like the Newegg how to build a computer series. Google Newegg and how to build a computer they'll come right up.
Greg N