I see this is over a year old now, but did you find the problem ? Working on a 05RS also, had the P0031 & P0134 codes. Checked the old sensor with a muiltimeter and the heater was dead. It should be around 10 ohms it said, this one was open.
Put on new O2 sensor, cleared the codes, it got rid of the heater code but still gets P0134 after a minute or 2 of driving. Testing the sensor shows it's outputting voltage when the car is running, but the computer is not seeing it. On the scope, the computer says the O2 sensor is flat at .02 volts.
The strange thing is the computer is putting back out about .350 volts on the sensor wires if you unplug the sensor and probe the car side of the plug and then 14 volts on the 2 heater wires, but that part is ok.
Im thinking the ecu may have failed to put putting out power on the sensor inputs ? Anyone else have to change a computer for this reason ?