But, if you're going to rise 40° on a climb before you get to the top and start down the other side I'd rather start that climb at 160° to rise to 200° than start it at 180° and rise to 220°.
Henry, I think your theory is flawed. You are not thinking about this correctly.
The maximum temp you get up to is dictated by the ability to dissipate the heat via the various media (water, oil etc. As the differential becomes greater between the operating temp, and the ambient temp, so the rate of transfer becomes greater.
In other words; If you start off as you say at 160 degrees and you top out at 200 degrees. In the next scenario you start at 180 degrees, it is most likely that you will still top out at 200 degrees.
Lets face it after 500 yards your so called 20 degree advantage will have already disappeared.
Once again, your thermostats are regulators in as much as they keep your operating temperature range narrow, in the range in which every thing has the correct clearances required for long engine life, and performance.
It will be interesting to see the results of what you are testing.