Old oil forced air heat only system (R/W wire only) - Is adding a C possilbe to use Wi-Fi
This is an interesting case since your oil burner control integrates the 24VAC control transformer.  Normally, you'd look for either a C terminal on the control, or the control transformer itself.  However, your control lacks a C terminal.  What it does have, though, according to the internal schematics from Honeywell's manual, is one of the F terminals for the flame safety photodetector (CdS cell) that goes back to the opposite side of the transformer from the upper T terminal that goes to the red wire.

You'll need a multimeter on continuity (or its lowest ohms range if you don't have a continuity buzzer on your meter) mode for this procedure.


Turn the service switch or disconnect OFF before starting to avoid damage to parts (it may be a switch on the unit, or you may need to use the circuit breaker to disable it).
Put one meter lead on the upper T terminal (the one with the red wire on it) and the other on each F terminal in turn.  The one that beeps (or reads low ohms) is equivalent to the C terminal, and can be used for a C wire connection.  The other is how the CdS cell connects to the internal circuitry, and will not cause your meter to beep (or reads a high resistance on the meter).
Connect the C wire to the correct terminal (it should be the bottom terminal according to the manual).
Hook up your new thermostat.
Turn the service switch or disconnect back ON.
Enjoy the new thermostat!