The short tinnitus that lasts just a few minutes is relatively common. Most common cause is stress and circulation issues. There seems to be no alternative name for the short tinnitus to differentiate between the permanent ringing.

I found that if it starts ringing in my ear due to stress or just spacing out during overthinking stuff, hyperventilating (increase blood oxygen levels) briefly and massaging my ear canal (increase circulation) from the outside helps to get rid of it more quickly. Maybe this helps somebody someday.