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I've done quite a few of the IPD-style flushes, and I recall (with a hot transmission) that it's closer to two minutes per half-gallon (I follow their advice of 2 quarts at a time, and I fill clear one gallon jugs), or one quart per minute. Given that the total capacity (including torque converter, which is included in this circulation) is approximately 7 quarts, or 1/7 the total amount per minute. But that's quibbling.
Regardless of whether the truth is closer to your or my estimates, that's not to say that the total volume of fluid will cool down to anywhere near the incoming fluid's temperature in some period, because the fluid is continually being reheated by both (1) the continuing operation of the transmission, and also (2) the latent heat of the hot transmission parts which will transfer to the briefly cooler fluid along the temperature gradient (hotter parts to cooler fluid), ultimately reheating the fluid. Only the continuous elimination of the heat through the primary (and auxiliary, if you have it) cooler(s), and remixing hot fluid with some (see, I avoided the word "small") cooler fluid keeps the overall fluid temperature below what it otherwise would rise to if the circulation through the cooler(s) stopped.
And my original point was simply that the cooler helps -- regardless of what you interpret as the meaning of the word "small" in my "...small amount at a time...."
Wasn't that fun? Anyway, let's turn our attentions to the festivities closing in on us -- happy holidays to you and all.
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