temperament / mood
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temperament
A person's general mental and emotional state or character; the way someone feels and thinks.
Er hat ein ruhiges Gemüt und lässt sich nicht so leicht aus der Ruhe bringen.
He has a calm temperament and doesn't lose his composure easily.
'Gemüt' belongs to the word family of 'Mut' (courage). While 'Mut' means bravery, 'Gemüt' describes one's inner mental and emotional state. The adjective 'gemütlich' (cozy) is also related and describes something that is good for the Gemüt.
Seine positive Art sorgt für eine gemütliche Atmosphäre.
His positive manner creates a cozy atmosphere.
To describe a person's character, 'Gemüt' is often combined with adjectives such as 'heiter' (cheerful), 'ruhig' (calm), 'sanft' (gentle), or 'sonnig' (sunny).
Meine Großmutter hat ein sehr sanftes Gemüt.
My grandmother has a very gentle temperament.
In the plural, 'die Gemüter' describes the mood of a group. Typical verbs in this context are 'die Gemüter erhitzen' (to inflame tempers) and 'die Gemüter beruhigen' (to calm tempers).
Die Diskussion erhitzte schnell die Gemüter.
The discussion quickly inflamed tempers.
The idiom 'jemandem aufs Gemüt schlagen' (to get someone down) has a fixed structure. The person who becomes sad is always in the dative.
Die ständige Kritik schlägt ihm sichtlich aufs Gemüt.
The constant criticism is visibly getting him down.
heart
'das Herz' and 'das Gemüt' can both have to do with feelings and a person's inner self. 'das Herz' is often used when talking about love, compassion, courage, or character. 'das Gemüt' refers more to someone's emotional mood or the way someone feels and reacts inwardly. It sounds somewhat elevated and often appears in fixed expressions, for example when something 'jemandem aufs Gemüt schlägt' (gets someone down). The words can be confused because both refer not to the body, but to a person's inner side. For love and compassion, 'Herz' is usually appropriate; for mood and emotional state, 'Gemüt' fits better.
Der lange Regen schlägt ihr langsam aufs Gemüt.
The long spell of rain is slowly getting her down.
Meine Nachbarin hat ein gutes Herz und hilft oft älteren Menschen.
My neighbor has a good heart and often helps older people.