Cool, cold, warm and hot (and variations thereon) have distinct, standardized meanings for fabric and clothing makers but not for North American washing machine makers. Washing machine manufacturers seem to have their own --- sometimes unpredictable --- notions which can vary from model to to model and from one wash program to another.

Fabric and clothing makers have an internationally agreed on standard. "Cold" and "cool" mostly mean the same thing, which mean temperatures at or below 86°F/30°C. That is what is meant when the fabric care tag says "cool" or "cold." That's what is meant when you see a fabric care tag with one of the international icons on it --- typically, a bucket with a single dot in it or the bucket icon with a single line beneath it.

"Warm" wash (bucket icon with two dots in it or two lines below it) means 105°F/40°C.

"Hot" wash (bucket icon with three dots in it or three lines below it) means at or above 120°F/50°C.

No such standards for washing machine manufacturers, at least in the North American market. It is pretty much the Alice-in-Wonderland/Humpty-Dumpty thing where the hot-warm-cold designations mean whatever the maker chooses at any given moment with any given model. For any given model, such as your GE, the setting might or might not track the fabric care standards.

Also, the hot-warm-cool settings may vary between cycles. There are some models where a manufacturer may have tried to game the Energy Star tests or other ratings by having the "hot" wash down as low as 90°F for a "normal" cycle and maybe some kind of non-specific "tap hot" on other cycles. IME, the programming for short "Quick" wash cycles sometimes seems problematic. From what I've read here and elsewhere (such as on the automaticwasher-dot-org site), warmer washes can boost the cleaning effectiveness of detergents and some manufacturers have seemingly tried to game product reviewers' tests of quick cycles by using warmer wash settings. Dunno if that is going on with your GE or not.

We once had a top-load washer that set temperatures by simply proportioning or switching flow from the hot and cold lines. IIRC, when the hot had just been used and was very hot, the "cool" wash water might be pretty warm. Also, My current FL washer also allows "quick" washes with either cold or warm rinses, as you choose. I think you have said that your GE does not offer rinsing temp choices on its quick washes?

Maybe you could test out the current temperature of the cold supply line by running a rinse and spin? Has the weather been very hot where you live? Maybe something was warming up the cold water feed?

Two of my washers have what is equivalent to a cool temperature ... between warm and cold. The ATC targets 30°C / 86°F.

Perhaps a rinse-and-spin would been more appropriate for your slacks?

Some washers have poorly-designed ATC such that they don't mix the incoming hot and cold flow directly but rather alternate full hot and full cold to attain an average ... so full tap-hot water may at times be spraying on the clothes during fill.

"Cool" will depend on your machine manufacturer. Our Miele FL owner's manual has charts with the various temps in every cycle shown in Celsius, so I converted and posted them on an index card over the washer in Fahrenheit. Helps me know which setting to choose. It has a built-in water heater so the target temps are consistent.

NO HEAT - whatever the tap cold temp is, depending on time of year

COLD - 86°

WARM - 104°

VERY WARM - 122°

HOT - 140°

SANITIZE - 160°

All rinses are in COLD. No other option for the user. After a HOT wash, though, the laundry can feel warm in spite of the COLD rinse, probably due to residual heat in the tub and laundry.

HTH

Cool washes will depend on the machine. I read this and was wondering if your machine happened to use a cool rinse as well to improve cleaning and reduce fill time when using the quick wash cycle? Just remind us what washer you have again please. If I recall correctly it is a newer GE HE TL.