My interpretation of the whole thing (I'm dealing with similar issues) is
that the O2 sensor works, no matter what temperature it's at, but the ECU is
programmed not to pay any attention to the voltage it produces until the
Temp II sensor says the engine is warm enough. Before that time, the O2
sensor produces voltage, but it's erratic.

I installed one of Ken Lewis' O2 sensor volt meters on my instrument panel
to have a constant monitor, and it's truly eye-opening to see what's going
on. When the engine's running rough and has no power, sure enough, the
oxysensor is putting out low voltage, indicating a lean condition.

If I were to replace the one-wire oxysensor system, it would be with a
four-wire, not three, because I think the ground needs to be absolutely
certain for these to work, and the old tailpipe structure seems a poor
ground at best. I grounded my O2 sensor with a wire and a radiator hose clamp.

The engine will run ok without the O2 sensor, but you'll spend a lot on gas...