Jeffrey, you're almost 100% right, but ...
Viscosity Index Improvers (VII) are a polymer of which the molecules are much like a tangle of string. When they are cold the tangle shrinks, when they heat up the tangle expands.
To make a multi-viscosity engine oil, like an SAE 5W-30, you start with a thin "base" oil and add the VII to it.
When the oil is cold the VII shrinks and the thin oil flows easily passed the VII molecules. Viscosity is "resistance to flow" so in this case the oil flows easily so is regarded as thin at a low temperature such as - 25 deg C, eg. SAE 5W.
When the oil heats up, so does the VII and it expands. Now the thin oil (which has also thinned out as the temperature has increased) has difficulty passing the VII molecules, it flows slower, so it is described as being thicker, eg. SAE 30. However this means it is thicker at the high temperature (100 deg C) that engine oil is measured at than the non-VII treated oil would be.
Now VII molecules come in different sizes. Larger molecules are more effective at slowing oil flow, or thickening the oil. So less of a large molecule VII needs to be used to get the same multi-viscosity effect. You have to use more of a smaller molecule VII to get the same oil thickening effect.
BUT, and ain't there always a "but"! The larger VII molecules get "sheared" down easily, that is they get chopped up into smaller VII molecules, and then there isn't enough of them to provide the oil thickening effect. So what was an SAE 15W-40 made from a large molecule VII will become something like a SAE 5W-20 or worse. This is called "permanent shear", it is irreversible.
A multi-grade engine oil made from smaller molecule VIIs will cost more - more VII and it is more expensive - but will resist shear down.
Now where I've said "VII thickens the oil", you should realise that at low temperatures any oil is really thick. What a VII does is slow down the thinning of an oil as temperature rises. Comparing just the thin base oil with the thin base oil plus added VII, the base oil will be slightly thinner at low temperature (the VII will thicken the base oil slightly). As the temperature rises both oils thin out, just that the VII treated oil will thin out less over the same temperature rise, until at 100 deg C the VII treated oil will be considerably thicker than the base oil at 100 deg C.
Then there is "temporary shear". This is where a VII treated oil passes between two moving surfaces, the piston rings and the cylinder wall is a great example. In that narrow gap the VII molecule tends to get stretched out from a tangle into a line and its oil thickening effect is lessened. However when it gets out of that stretch zone, the VII moecule returns again to its tangled state and its oil thickening effect returns. Thats temporary VII shear.