The mechanism that triggers shivering with fright or any emotional stress, is different from the one that causes the trembling man in the cold.
When frightened brain (or rather, the Department of the brain called the hypothalamus) generates an alarm signal to the adrenal glands. In response, they throw in the blood of special substances - hormones adrenaline and cortisone (they are even called "stress hormones"). The purpose of these same hormones quickly to mobilize the body to prepare it for the upcoming exercise - flight, protection or attack. They cause increased blood pressure, increased heart rate, sweating and here we come to the answer to the question - increased muscle activity to such an extent that some of the muscles even begin to tremble.
By the way...
Not always the end result of an emotional outburst is running or other types of physical activity. Often in modern society, they are replaced by verbal duels, and more often need to be able to control his emotions. However, the mechanisms for increasing the readiness of the organism to physical and nervous stress that we have inherited from our ancestors, are included regardless of our consciousness. Such innate protective response of the body is called unconditional reflexes. The objective of the launch of any unconditioned reflex is to bring the body back to normal.