Usually when I play long sessions of this game. I hear a single beep from the pc speaker. When I ignore it and keep playing, it becomes a loud screech and had to turn off the game in order for it to end. Anyone else have this problem?

It means that they are breaking through. Don't let them.

Is that the heat sensor on the inside of the case?

Nope. It's done this before back then on my previous computer too. At the time the game was orignally released.

... PC speakers still exist?

Yeah, it just happened to me a few days ago after I had been playing LOMSE for a few hours. I just exited the game and ejected the disc and it stopped.

Most every PC still has a piezo buzzer to help with diagnostics during boot-up.

Just a few months ago, I bought the components to build a new PC, and one of them was a piezo buzzer. I think, at least, that it came with the PC case rather than the motherboard.