NERVOUS is good if you mean that they're worried or tense. It doesn't mean that they become upset, like нервный does in Russian. BAD-TEMPERED is best used as a general description and not a situational one. When we refer to a moment where someone who's normally positive and nice becomes "bad-tempered" because of circumstances, it's better to use CRANKY. So my recommendation would be: People can/tend to become cranky when THEY'RE stuck in traffic. -or- BEING stuck in traffic can make people cranky. -or- Being stuck in traffic can produce road rage.

Additionally, you can say that being stuck in traffic can make people LOSE THEIR TEMPER.

He got crazy /mad in traffic. Это идиоматично?

mad 👍🏼

Thanks, good to know!

He got mad in traffic. Как это будет на русском?)
Он теряет контроль/ выходит из себя в пробках.?

Он теряет контроль/ выходит из себя в пробках.?

in traffic - это не "в пробках"

Zoya is correct. Sometimes we call traffic jams “bad traffic” or just
“traffic.” https://idioms.thefreedictionary.com/stuck+in+traffic