warm
Having a pleasantly high temperature that lies between cool and hot.
Die Suppe ist noch schön warm.
The soup is still nice and warm.

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Having a pleasantly high temperature that lies between cool and hot.
Die Suppe ist noch schön warm.
The soup is still nice and warm.

'Warm' belongs to a word family related to temperature. Related words are the noun 'die Wärme' (warmth) and the verbs 'erwärmen' (to warm something up) or 'sich aufwärmen' (to warm up before sports).
Die Wärme der Sonne fühlt sich gut an auf der Haut.
The warmth of the sun feels good on the skin.
In connection with clothing, 'warm' is often used in the instruction 'Zieh dich warm an!' (Dress warmly!). This is very common advice when it is cold outside.
Es schneit! Zieh dich warm an, bevor du rausgehst.
It's snowing! Dress warmly before you go outside.
'Warm' can be used metaphorically for feelings and social interactions. It then describes a warm-hearted, friendly, and welcoming atmosphere or person.
Sie hat eine sehr warme und freundliche Ausstrahlung.
She has a very warm and friendly presence.
The adjective 'warm' is also used to describe colors. 'Warme Farben' (warm colors) are typically shades of yellow, orange, and red that are perceived as cozy and inviting.
Für das Schlafzimmer haben wir warme Farbtöne ausgewählt.
We chose warm color tones for the bedroom.
The expression 'mit jemandem/etwas warm werden' means to slowly get used to a person or situation. It is very often used in the negative: 'nicht warm werden' (not to warm up to).
Mit meinem neuen Kollegen bin ich noch nicht richtig warm geworden.
I haven't really warmed up to my new colleague yet.
cool
'cool' and 'warm' are opposites when it comes to temperature. Here, 'cool' means pleasantly cool or refreshing. This use is less common in German and sounds a bit closer to English. 'warm' means a pleasantly high temperature, so not cold and not hot. For temperatures, people usually use 'kühl' rather than 'cool' in everyday German, but as the opposite of 'warm', 'cool' can appear in certain casual situations.

Zieh eine Jacke an, damit dir auf dem Heimweg warm bleibt.
Put on a jacket so you stay warm on the way home.
Nach dem Sport tut ein cooles Getränk richtig gut.
After exercising, a cool drink really hits the spot.