Unfortunately not. They're all soldered in on modern laptop boards. Even those that you can change have very specific chips they'll take and it's not as easy as a desktop to just plug and play a new CPU.Is it possible theoretically to buy a new processor then ? (like is the swap operation simple ?). I figure you'll tell me it's best to just buy a new computer then, but a really good processor here would be about 500€, still better than a computer (although I'd sell my current one obviously...). Eh. Can't be screwed to start all over again, reinstalling all the software etc...
You could sell it ASAP as it's a pretty nice laptop and still valuable, just not geared for your use. That or make do and save for something nicer (probably what I'd do).
A cooling pad might help keep the CPU from throttling as much during heavy usage.