Does anyone know if there is a digital thermostat from which I can control both the central heating and the fireplace?

What fuel source does your fireplace use?

Fuel is Natural Gas

Actually, both fireplace and central heater use natural gas.

How is tyour fireplace ignited?

If the pilot is on, the fireplace ignites if the room temperature is below the desired temperature that you set in the thermostat.

If the pilot is off, I need to manually ignite it pushing two buttons simultaneously.

Does anyone know if there is a digital thermostat from which I can control both the central heating and the fireplace?

This is a combination I would not recommend!!