What to Do If a Child Suddenly Develops a Fever at Night?

The baby suddenly developed a fever at night, could it be from being chilled during the day? I measured the temperature twice and it was 38.5! In the morning, I measured it two or three times and it was 38.3, once 37.8. I gave him some fever-reducing medicine and ate some steamed bun with pumpkin cake, but then he fell asleep again! Just measured it again and it was 37.9! Should I take him to the hospital in this condition?
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