Most O2 sensors have their own built in heaters. If the o2 sensor fails to heat up, the hot exhaust gas will kill the sensor thus making the car run in OPEN loop, which means the ecu does not use the o2 sensor to aid in fueling.
You can also test the ECT sensor to make sure it is getting the proper voltage. These specs can likely be found online or in the service manual if you have one. If you are not getting proper voltage at the ECT sensor, the ECU will not be able to give the proper fueling. During the startup process, the engine runs in open loop until the o2 sensor is heated and until you meet a specified coolant temperature threshold. Once you get to operating temperatures (roughly 190-200*F) the engine will switch to closed loop.
Start the car and use a multimeter to test its voltage. Narrow band o2 sensors run 0-1volt.
good luck.