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Probably doesn't matter, as long as you're consistent. Either always cold, or always after a specific amount of warmup.
My protocol: TrainerRoad ramp test every 4 to 6 weeks, do my standard BC 20 minute warmup, calibrate the Kickr then do the test. I don't calibrate outside of that.
Having measured with PM pedals, crank + Kickr at the same time over several workouts, the Kickr reads about 10% higher (so easier on you) for the first 20 to 30 mins of a workout. The pedals and crank were consistent throughout, 30 to 40 mins in they all line up.
I always use the Kickr for power indoors, as a result of my testing I used to bump my workouts up 10% for the first half, but eventually forgot about it and just rode them as is. I train at 7am straight out of bed so easing into Vo2 max ain't a bad thing really.
The idea of the calibration is to get the same level of resistance for each ride. Yes, calibrating cold/warm are going to be different values that's why you should calibrate after a standard warmup. If it's way off you can calibrate to the same value but adjusting the tyre clamp pressure, assuming it's the same as the Computrainer calibration. The actual difference is only a few percent but this becomes noticeable when you're doing an extra 10W at your supposed threshold or your VO2s are all 15W harder, etc.