Good question. Going thru a little automotive education, I'd say to a degree. At least in automatics, fluid gets pump'd around. That fluid is thinner when hot. Cold transmission fluid can be anywhere from 40-60F and heat up to 200-260*F in normal operation (this is more of a manual fluid spec, auto's have a radiator compartment oil cooler that keeps temps more regulated). Colder fluid more resistance to pump thru oil passages in the transmission.
ATF is Wt10 oil. Pretty thin. but not 5w20 thin.
Manual transmission use 75w-90 which is more of a 10w30 (old honda spec)
Manuals dont pump fluid thus a little more efficent. (someone can add here, but off the top of my head a convention manual is 85-95 efficient and autos are 80-90%, newer pump less fluid and work better)
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