cold
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cold
The state of low temperature; the absence of warmth. It describes a physical property of the environment or of an object.
Trotz der Kälte von minus zehn Grad gingen sie spazieren.
Despite the cold of minus ten degrees, they went for a walk.
'Die Kälte' (the cold) is the noun corresponding to the adjective 'kalt' (cold). The pattern of forming a feminine noun from an adjective with the ending '-e' is common in German, e.g. warm → die Wärme (warmth), groß → die Größe (size).
Die Kälte des Metalls war unangenehm auf der Haut.
The coldness of the metal felt unpleasant on the skin.
When referring to temperature, 'Kälte' (cold) is often described with adjectives such as 'eisig' (icy), 'bitter' (bitter), or 'streng' (severe). People can 'vor Kälte zittern' (shiver from the cold) or 'sich gegen die Kälte schützen' (protect themselves against the cold).
Zieh dir eine dicke Jacke an, um dich vor der Kälte zu schützen.
Put on a thick jacket to protect yourself from the cold.
In its figurative meaning, 'Kälte' (coldness) often describes distant behavior. Typical collocations are 'emotionale Kälte' (emotional coldness), 'Kälte zeigen' (to show coldness), or the sentence 'Zwischen ihnen herrscht Kälte' (There is coldness between them).
Seine Worte waren voller Kälte und Ablehnung.
His words were full of coldness and rejection.
The context reveals whether temperature or feeling is meant. Words like 'Grad' (degrees), 'Winter' (winter), or 'frieren' (to freeze / feel cold) point to the literal meaning. Words like 'Gefühl' (feeling), 'Herz' (heart), or 'Beziehung' (relationship) point to the figurative, emotional meaning.
Die Kälte des Winters macht mir nichts aus.
The cold of winter doesn't bother me.
temperature
'die Temperatur' and 'die Kälte' both have to do with warmth and weather. 'die Temperatur' is a neutral measured value: it can be high, low, or normal and is often given in degrees. 'die Kälte' only means the state of being cold or the absence of warmth. The words can be confused because both occur in weather reports and in everyday life. In practice: if you mean a number or a measured value, 'Temperatur' fits. If you want to describe that it is unpleasantly cold, 'Kälte' is a better fit.
Wegen der Kälte zog Maria eine dicke Jacke an.
Because of the cold, Maria put on a thick jacket.
Vor der Reise habe ich die Temperatur in den Bergen geprüft.
Before the trip, I checked the temperature in the mountains.