OK, my two cents.
First, definition of thermal breakdown: about a certain temperature additives and base oils deteriorate much more quickly. Additives in synthetics and minerals oils are essentially the same, perhaps in a little different ratio. That number is around 300F, perhaps another 50F for synthetics, but if you are up there... something else is going to melt also. Anyway, thermal breakdown is when the oil starts to polymerize and turn dark, form varnish, deposits, and usually it thickens.
Normally, as an oil get hotter, it gets thinner. The viscosity index improver is an additive that decreases this thinning rate. So even though an SAE 0W40 is thinner at 100C than at 0C, it isn't as thin as it would have been if it didn't have the VII.
Multigrade oils are formulated by selecting the base oil in order to meet the low temperature properties and the amount of VII is added to meet the high temperature viscosity. Note that it is not the other way around - it is not an SAE 40 that somehow behaves like a 0W, it is a 0W that is thickened to behave like an SAE 40. So a poorer quality VII, one that is not shear stable, will thin out more and permanently at high temperatures. This is the opposite result of thermal breakdown, where it will thicken!
Castrol is to blame for their ads about thermal breakdown, viscosity breakdown and so on - technically all things that are important, but confusing since they run all the ideas together.
One last lesson - a synthetic base oil has greater inherent multi-grade properties than a base oil, so you need less VII to formulate a synthetic 5W-30 than a mineral 5W-30.
What does all this mean in regards to the 0W-40? If the VII is not shear stable, in time, it will behave like a 0W-30. The odds of a Mobil synthetic oil doing that are reasonably low; it's a premium product, it carries European claims, both European and US engine oil performance specs require some level of shear stability, and as noted, there is less VII in the formulation, so and degradation will have less of an effect.
ERDOC, you are otherwise correct - thin at start up and thick (relatively) when hot. That is ideal.
Steve, your question is more complicated. A 10W30 is not common in Europe, so it's unlikely to have Euro performance claims (or as many.) If it's recommended for a US market car, the oil drains might be shorter than the same car in Europe. A 0W-40, however, is almost specific to Europe, so it will be formulated for that market, that OEM, and maybe almost that car. While the first impression might be the 10W30 is too thin, it might very well be that the 10W30 additive package is not as robust as the 0W40 additive package. (No, I didn't look it up yet.)
