I don't have time to check the logs right now, but it could be your sensor heating up too much or something.

Technically the car should be running while the sensor is powered up or it could be damaged... at least according to my innovative gauge manual. Apparently they need the exhaust going to by to cool them or whatnot. So, just try not to leave it in the 'on' position for a very long time without running the motor. Seems like they would give you a tach input or something if it was that big of a deal, but who knows.

As for the numbers going up, it could be the sensor warming up, but it should hold steady while running. If you turn the car off, it will creep up as the mixture in the exhuast creeps more and more toward standard atmosphere, which is infinity to 1 or something AFR, so that is probably okay. The reading going up while you run sounds like possibly it is leaning your out because warm up enrichment is not adding as much fuel as the car gets warmer. You should be able to view that field in the log to see if that is changing while you go lean. Check the curve and make sure it has sane values in it, I think very cold gives 150% fuel, all the way down to 100% fuel at operating temp.

You can also check to see if it is the wbo2 causing a problem by looking at the pwm of your injectors to see if they are constant. If RPM, MAP, and IAT are pretty steady, a constant PWM should yield a constant AFR. That assumes the injectors are working as they should of course.