The answer already provided by @fred_dot_u at the time of writing is good, so I won't rehash what they already said, but will try to answer your questions from another angle:

I'm wondering whether the degree to which the filament contracts is proportional to the amount that it cools.

Yes. This is generally true for any solid material. This property is linked to the fundamental nature of matter in the way we understand it today.

If the answer is yes, then wouldn't it suggest that a lower printing temperature might reduce warping-as the temperature interval over which the filament cools is smaller?

Shrinkage is the root cause of 3D prints warping, however warping itself happens because of the differential in temperature between layers: when a hot layer is extruded on top of a cold one and begins to contract, it will apply a compressing force on the layer underneath, bending it.

In fact - if warping were a function of shrinkage - an enclosure would do no good: sooner or later the print would cool down to room temperature, and would warp. The reason why - contrarily - an enclosure works, is that it limits the differential in temperature between layers (which causes warping) and lets the entire print too cool uniformly and slowly afterwards.

So, would...

...a lower printing temperature reduce warping? [...] Or perhaps the difference is negligible?

Nothing beats real world data, especially when the issue has so many variables that are difficult to account for, as in 3D printing, so I would invite you to simply try to print the same model twice, only changing the printing temperature (and of course making sure the environmental temperature is the same), and see if it does.

From a theoretical standpoint, I could argue both ways.

On one end, I could argue that this is nothing different than using an enclosure set at a slightly warmer temperature than the environmental one, so it will reduce warping (even if by not much).

On the other hand, I could argue that until the filament is solid enough, it won't be able to "pull" the layer below, so it doesn't matter if the extrusion temperature (fluid state) is 230°C or 210°C, if until 190°C the filament won't begin to "pull". So warping will be identical.

Also, I see a lot of emphasis placed on good first layer adhesion. Is this still an issue if you are printing on a raft?

Yes, as also the raft has a first layer that needs to adhere to the build plate. Rafts typically have a discontinuous and over-extruded first layer over a large area, which definitively helps with adhesion, but you still have to make sure the raft sticks well. In my experience it is far easier for a raft to come off the build-plate than for the model to come off the raft. YMMV though, as the material of the build-plate, and the slicer can dramatically affect this.