Device to Monitor Fireplace Status (On or Off)

You don't say, but I assume it's gas?

Not sure I'm clear, what is the normal way you turn the fireplace on/off. Via the thermostatic remote?

This thread probably has a couple ideas you might be able to leverage, similar discussion we just had. It's about monitoring a gas stove for on/off, but the several of the solutions proposed might actually work better on a fireplace application.