Heater element in the O2 sensor, nowt to do with the cabin heater

O2 sensors only give an accurate output when they're at a very specific temperature window - this is usually maintained by the gas flow when you're underway and the engine is doing some work, but at light loads and immediately after starting the car (and the 3.2 is generally 'lightly loaded') the ECU turns on a heater element within the O2 sensor to maintain the temperature of the core.
The heater element is essentially a big resistor - the same principle the heater rear screen works on - they get very fragile with age and use so they're easy to brake in an old sensor when removing & refitting it, but generally fairly tough in a new unused sensor (thermal/work hardening of the heater element, I suppose).
They have a fairly beefy power requirement so often have a fuse of their own or a fuse per set of O2 sensors - not sure how it's wired on the Omega.
But the long & short is - if the heater element isn't being fed with power (all the ECU knows is it's 'open circuit' - it assumes it's the sensor at fault but it could be a break anywhere in the wiring to the sensor or the feed fuse) then the O2 sensor will be very slow to respond and the ECU will flag that fault as well.