Adding the c wire to a two wire system

After looking closely at the images you've supplied, this is what it appears is going on in the last photo.

From what I know about HVAC systems, I would guess a broader view of the system would look something like this.

• The transformer supplies power to the thermostat through the RED wire.
• The BLUE wire serves as the COOL call from the thermostat.
• The BLUE wire connects to the WHITE wire, which is connected to the coil of the contactor in the condensing unit.
• The GREEN wire is the other side of the contactor coil.
• The GREEN wire connects to the BROWN wire, which is the other side of the transformer (C).

When the thermostat calls for COOL, the BLUE wire is energized. This energizes the WHITE wire leading to the contactor, which pulls the contactor closed. The GREEN wire connects to the BROWN wire, which leads back to the transformer, thus completing the circuit.

Therefore, if you want to use the YELLOW wire as C. You should include it in the twist-on wire connector with the GREEN and BROWN wire.

You'll just want to make sure the transformer is sized properly to supply the additional current draw of the thermostat.

If it were me, I'd rewire it so that the YELLOW wire was the COOL call, and the BLUE wire was C. As that's a more common color coding.

From the pic, I'm guessing the transformer is the black device under the junction box. Looks yellow and purple coming off of that, you're connecting to the yellow, so the purple would be the common. To be sure, you'd want to connect a multimeter and verify the voltages to ground. It would also be helpful to find the wiring diagram for your boiler to be sure you're interpreting these wires correctly.

Assuming purple is the common, you'd run your wire to that, preferably through that wiring block where the other thermostat wires are connected on the left. There's no issue connecting the common to multiple places.