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Are there any known controlled tests, showing a difference in time-to-temp between 0W-xx and 10W-xx (with "xx" being the same)?
Not that I'm aware of. Thicker oils (again we have a self correcting "phase shift" that confounds any absolute view) are harder to shear and therefore generate more heat due to friction. My thought is that under like conditions, a thinner oil shears easier/thinner and can conduct/convect heat easier.
..but that I think (under like conditions) would result in a different normalized temp and not a difference in time to temp. At least those were my observations.
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When the oil is cold, would the oil pump bypass be in relief?
How cold? How high a volume? How high is the starting visc due to the OEM requiring a 40 weight at operating temp? Lots of variables. I've seen some pushrod generic engines I've seen, the pressure never came off of the relief. Flow was totally variable based on visc. It wasn't common, but I've seen it.
If you're at -30C with a high visc oil with a higher volume pump (or even a common volume pump) ..probably. Doug Hillary finally connected the dots for me on why many Euro's have 30+lb bypass limits on their filters. It's because they may be up against pump relief for 15+ minutes and don't want most of their engine's life being spent with partially filtered oil.
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If it is, a thinner cold oil would result in more oil flowing through the engine, transporting more heat around, getting faster to operating temp.
...or soaking up/shunting/rejecting more heat at the same time. It's a "as it spreadeth ..it taketh away" view. Under the believe that it distributes it better, it would also dump it easier too. In the same rationale, you would have to say that thicker oils, while not as readily soaking up and distributing heat, don't allow it to escape as easily.
That's why I think it's a wash.
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Thinner faster flowing oil transports it better.
As opposed to thicker faster oil, I'll probably agree. The thing is, if you're not in relief, the oil flow rate is identical. You may have some intermediate velocity difference in how fast it reaches the pan, but it won't exceed the mean velocity of the pump, unless you such the pan dry and have the valve covers fill up with oil (don't laugh, some SBC's would do this).
If you are in relief, then the flow rate is slower ..and so is the dwell time ...slower alterations to bulk oil temps. Again, a wash.
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Personally I did notice a difference between 5W and 0W oils, both 30 weights.
With the 0W oil the engine runs noticeable smoother just after a cold start.
Quite possible.
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I'll defend my 0W oil
..and so you should, young man!! (visions of as if you just said "I respect my parents"
)