bamedo yeori gyesok namyeon eunggeupsire gaya hae.

밤에 means at night. Adding 도 gives 밤에도, which means also at night or even at night, depending on context.

Here, 도 adds the idea that the fever continues during the night too, not just during the day. So it emphasizes that the symptom is still happening at night.

• 밤에 = at night
• 밤에도 = also at night / even at night

In Korean, 열이 나다 is the natural expression for to have a fever or literally for fever to come out / appear. This is just the standard Korean way to say it.

So:

• 열이 나다 = to have a fever
• 열이 있다 would sound unnatural for this meaning

This is a good example of a Korean expression that does not match English word-for-word. Even though English uses have, Korean uses 나다.