The thermostat is simply a switch; inside it is a bulb with some
contacts and some mercury that rolls back and forth inside the bulb to
make and break contact as the bimetallic spring that holds the bulb
expands and contracts with the ambient temperature. One can remove the
thermostat, twist its 24 volt red and white wires together to get heat
without any control - just ON.

The furnace's gas valve is opened by power from the thermostat, the
furnace lights and when the fire box is warm the blower for the ducts
will start to distribute the heat. The fire is cut off when the
thermostat switches to OFF and the furnace blower runs until the fire
box cools down when it shuts off.

That's basically how it works.

You said the furnace was upstairs. Is there another furnace for
downstairs? If so are there timers on either furnace?