There are 2 sensors - 1 for the gauge, and another one to tell the ECU what the coolant temperature is.Really, you shouldn't be pushing the engine before it is warmed up properly (and letting it idle for several minutes first WILL NOT warm it up).
AND IT WILL HAVE NOTHING TO DO WITH THE O2 SENSOR!!!!!!!!!!!! For the 2,345,987th time, the ECU only reacts to the O2 sensor on constant throttle / cruise conditions. Under acceleration, the ECU ignores any input from the O2 sensor.
The engine is cold, it isn't working to optimium - live with it!