Why thinner oil improves fuel economy
 

The VI additives have the effect of keeping the oil from thinning excessively when heated. The actual mechanics of this system are a little more complex in that these additives are added to a thinner oil so that it will be fluid at a cold temperature. The VI additives then prevent thinning as the oil is heated so that it now can pass the SAE viscosity rating at 210. For example; if you have a SAE 10 motor oil it will flow like a 10W at the colder temperature. But at 210 degrees it will be a SAE 10 giving us a 10W-10 or SAE 10 viscosity rating. Obviously this is good at cold start up, but terrible at engine operating temperature especially in warmer climates. But by adding the VI additives we can prevent the oil from thinning as it is heated to achieve higher viscosity numbers at 210 degrees. This is how they make a petroleum based motor oil function for the 10W-30 rating. The farther the temperature range, like with a 10W-40, then more VI additives are used. With me so far? Good, now for the bad news.
From Motor Oil Viscosity Grades Explained in Layman's Terms

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I tend to cast a "doubters eye" upon anything that AMZOIL™ spews...

There waa a post about study Cummins diesel did on thinner oils on here a few years ago.
Going from traditional 15w-40 oil to the thinnest 0w-20 on the market saves about 3%.
But then the valve train wore out in about 2/3 the normal time. So probably not really worth it.

As you point out the failur savings are pitiful a penny per thousand miles whereas the extra horsepower required by the oil pump due to higher viscosity can be worth dollars per hundred. Every start is a cold start unless your oil is at operating temp it will take more powerto move the oil , than in a few minutes when completely warmed up. The colder the start the bigger the penalty on a parabolic curve.
Oilpan this point is why you ,I and many others go through such grate lengths to warm the oil in addition to the standerd water heater.

Old tele man
They even admit they are not large oil co. (There still an oil co.).
"As more and more large oil companies switched their "synthetic" motor oils to the less expensive/more profitable Group III (3) base stocks it has become much easier to identify which are PAO based true synthetic. Of the large oil companies, only Mobil 1 Extended Performance, as of this writing (12-16-2012), is still a PAO based true synthetic. The rest, including regular Mobil 1 and Castrol Edge have switched to the cheaper/more profitable Group III (3) petroleum based "synthetic" motor oil. AMSOIL Synthetic Motor Oils are PAO based true synthetic motor oils with the exception of the short oil drain OE and XL synthetic motor oils sold at some Auto Parts Stores and Quick Oil Change Centers.( This sounds like unless you buy direct from supplier even Amsoil is cutting corners as well) This leaves more than 20 PAO based true synthetic motor oils manufactured and marketed by AMSOIL with only a few Group III (3) based synthetic motor oils identified by the "OE" and "XL" product name."

For what it's worth, 10k miles on Mobile 1 0w20 in my engine and it was still basically a 0w20; viscosity had not changed measurably. I'm inclined to think that viscosity modifiers, at least in my case, will not break down before other additives are depleted.

Right now I'm running Honda's Green Oil, which is considerably thinner than 0w20. I'll probably have an oil analysis done in a few months for you to look over.

I'm gong to have to agree that this is a great reason why pre-warming, or fast warm up solutions are so important. Not just for engine oil, but trans fluid as well.