kühl
cool
A temperature that is felt as pleasant or slightly cold, but not freezing.
An einem kühlen Sommerabend saßen wir noch lange draußen.
On a cool summer evening, we sat outside for a long time.

cool
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cool
A temperature that is felt as pleasant or slightly cold, but not freezing.
An einem kühlen Sommerabend saßen wir noch lange draußen.
On a cool summer evening, we sat outside for a long time.

The meaning of 'kühl' (cool) depends strongly on the context. If it refers to weather or drinks, it is about temperature. If it describes a person or a reaction, the distant, emotional meaning is intended.
Die kühle Brise am Meer war sehr erfrischend.
The cool breeze by the sea was very refreshing.
The expression 'einen kühlen Kopf bewahren' (to keep a cool head) is a fixed unit. It means to stay calm and rational in a stressful situation.
Als der Computer abstürzte, hat sie einen kühlen Kopf bewahrt und das Problem gelöst.
When the computer crashed, she kept a cool head and solved the problem.
In connection with temperature, 'kühl' (cool) is often used for weather, air, or drinks. Typical combinations are 'kühles Wetter' (cool weather), 'ein kühler Wind' (a cool wind), or 'ein kühles Getränk' (a cool drink).
Nach dem Sport trinke ich gerne ein kühles Wasser.
After exercising, I like to drink a cool water.
When 'kühl' (cool) describes a person or their behavior, typical combinations are 'ein kühler Empfang' (a cool reception), 'ein kühles Lächeln' (a cool smile), or 'kühle Distanz wahren' (to maintain cool distance).
Ihre Reaktion war eher kühl und abweisend.
Her reaction was rather cool and dismissive.
You can recognize the meaning connected with colors from words like 'Farbe' (color), 'Farbton' (shade), or 'Einrichtung' (interior design/furnishings). It then refers to colors like blue or green.
Das Wohnzimmer ist in kühlen Blautönen gestrichen.
The living room is painted in cool shades of blue.
cool
'cool' and 'kühl' can both have to do with calmness or with low temperature. For temperature, 'kühl' is the normal German word: 'ein kühler Abend' (a cool evening) or 'ein kühles Getränk' (a cool drink). 'cool' sounds more modern or closer to English here and is less common. For people, 'cool' colloquially means that someone stays calm and composed. 'einen kühlen Kopf bewahren' (to keep a cool head) means something similar, but sounds less youthful and more like a fixed expression. The words can be confused because both sometimes mean 'calm'. For weather, air, and drinks, 'kühl' is usually the right fit; for a relaxed, composed impression, 'cool' often fits well.

Am Abend wird es im Garten ziemlich kühl.
In the evening, it gets quite cool in the garden.
Trotz der schlechten Nachricht bleibt sie ganz cool.
Despite the bad news, she stays completely cool.