The heated O2 sensor is powered 100% of the time the engine is running, no time delays or controls. Yours is heated to temp by the exhaust gasses only. How are you determining when the system is going into closed-loop (feedback) mode?

Your engine should not be running excessively rich during warmup. If it is, then either the warmup regulator is out of calibration (or contiminated port) or the basic mixture adjustment is set too rich.

Adding the heated type O2 sensor makes sense if you have to replace yours anyway, but the improvement will be quite minor, unless you are profiling the emissions during the warmup cycle. There is only a 1-3 minute difference in getting to operating temp between the two systems, partly dependent on the actual location of the sensor.