Oxygen Sensor Heater Circuit Issue

So I got a P0031 code for my 2012 Prius C. The upstream O2 sensor. Easy enough. I bought an new one and installed it. I did an ECU reset, started the car and immediately noticed an improvement in the mileage. The following morning, however, I saw that the mileage and returned to being as bad as before I changed out the O2 sensor. The engine light did not come back on, but I thought I would connect the reader and see if anything was there. The oxygen heater circuit code came up again on the code reader, even though the engine light had not come on again. I figured I had got a bad O2 sensor, so I bought another one and installed it. Even went with a different brand. The first one was a Bosch. The second a NTK.
Anyway, I installed the NTK and reset the ECU. Car started up, no engine light and, again, the mileage had improved significantly. The following day, back to bad.
One thing I have noticed, because of the time of the year with the colder weather up here in Calgary, whenever I drive in the morning, when it is cold, I get bad mileage. In the afternoon, after it has warmed up outside, I get much better mileage. This leads me to ask, is there a fuse or relay that controls the heater in the oxygen sensor? It appears that this is all related to temperature, yet I cannot find any information about it anywhere.
Oddly, my daughter is having the identical problem right now with her 2012 Kia Optima hybrid. Cold weather = bad mileage. Hot weather = good mileage. We changed the O2 sensor on her car as well. There has to be a common issue here that I have overlooked. Has anyone out there found a solution to this? Has anyone had the same problem?
I'm going to look at it again today. If I find anything out, I will update here.

 

Thank you for your input.

On a whim, I went out and purchased a downstream O2 sensor and installed it this morning. The original trouble code I received was for Bank 1 Sensor 1 (upstream), not 2, but I figured what the hell. As it turns out, this corrected the mileage issue I was having on my Prius C. Hopefully it will be the same fix for my daughter's Kia.

Take care

 

PROBLEM SOLVED
I ended up replacing both O2 sensors and the problem was remedied. Even though I did not get an OBD code for the downstream sensor, it seemed like a prudent course of action.

I just wanted to add this note for anyone else who finds this blog post in the future, I've had my Prius C since day 1 and never had mileage issues like this prior to the O2 sensor problem. Up until now, I averaged around 4.5 liters/100km (52 MPG). When the O2 sensor trouble occurred, it got as bad as 7 liters/100km (33 MPG). I want to point out, I've never seen it get that high in the seven years I have had the car. Now with both O2 sensors replaced, I'm down to 3.7 liters/100km (65 MPG). Even better than when I originally bought the car. Never been able to say anything like that about any vehicle. LOL