It doesn't really matter- you can do it either way. It is easier for me to add my strike water at 180 degrees and then let it cool to my strike temperature but you can preheat with other water and drain it. Especially in the winter, a cooler can suck a lot of heat out of the water!
I do essentially the same thing. But . . .
About three years now into all grain, I've had to change my setup a couple of times meaning, different preheat routine etc. The last time, I decided to do this 'scientifically.' I put a measured amount of hot water into my mash tun, recorded the water temp just before pouring in, and then let it sit about one hour and took the temperature again. By multiplying the change in degrees by the number of quarts of water used I calculated the amount of heat (in degree-quarts) that my setup absorbed. In this case (a brand new, 52 qt Coleman Xtreme with a fairly large copper manifold) the system absorbed 300 degree-quarts.
Why bother?
I brew a range of beers from LG bitters with 8 lbs of grain, to HG IPA with 16+ lbs grain. So, the amount of preheated strike water going in to the cold mash tun varies by up to a factor of 2. Previously I always added about 15 degrees to the strike water, but noticed that it sometimes wouldn't drop to strike temp without some encouragement, or would overshoot and I'd be running out to fire up the kettle again. It takes a surprising amount of boiling water to raise temp by a couple of degrees, messing up your water to grain ratio. It was no act of genius to notice that the small volume batches tended to overshoot on the way down!
Now I calculate the preheat temp by dividing 300 by the number of quarts of strike water to give degrees lost to preheat. For small batches this can be up to 30 degrees, which was surprising, but so far, I've found it much easier to hit the strike temperature within reasonable times with this additional step. And I don't have to run for boiling water anymore!
There are some assumptions of course.
First, that you have a good cooler that will reach equilibrium temp and hold it fairly steady. Then, after one hour, you have probably hit that equilibrium so you are really calculating the thermal absorption of your system, and not some arbitrary number on the way back down to room temperature (which you are, in fact, but you know what I mean). It seems most of us have a pretty good cooler by now that will hold mash temps if we are batch sparging.
Second, that in your experiment, you are using a 'typical' volume of strike water and a 'typical' temperature, like 15 qts at 180 degrees. I doubt your results will be valid if you put in 2 quarts of boiling water, or fill it to the top with 120 degree used bathwater. Might make an interesting experiment though.
Finally, that the ambients are not moving around too much. I brew in the same place in the basement now, always, although I used to move around and had noticed big changes in the amount of heat absorbed (and temperature loss during the mash during the winter, which is why I moved indoors in the first place). You may want to calibrate for multiple ambients if you prefer that kind of variety in your brew days.
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