not a lot left that you can change.
It's unlikely to be the LCD or the hard drive.
The processor will have had new thermal paste when the logic board was changed out, but that does not rule out failing fans.
Had you not mentioned that the board had been changed out, I would have gone with it as that is where the graphic card is.
If the MBP is under warranty, back to the shop it goes until it is either fixed correctly or it's replaced
A month ago I was listening to you tube and suddenly it sounded like a record skipping. My computer froze and started to be erractic from that episode on. I brought it in and they said it was a Logic board. It ran ok for 3 weeks and the same thing happened. Music started skipping and it froze up. It seemed to be running hot to me. Then when I rebooted the apple logo was a hazy red and when the desktop came up it had red stripe vertical lines running top to bottom 12 across. I waited another hour and it booted up (sow) but now its running normal. Any ideas? seems like my Apple store missed the diagnosis.