There are several reasons for sweating at night, both in children and in adults: having nocturnal sleep apneia, seizures or hypoglycaemia (low blood sugar) or infectious diseases, endocrine diseases, an insulinoma, for example, or psychiatric disorders.
Apart from these cases, which always imply going to the doctor and a diagnosis of exclusion, there are some a few unexplained symptoms of night sweats. First of all, in order to sleep, one should not be either too cold or too hot. Cold or hot feet prevent falling asleep and induce awakenings during the night.
Children can, indeed, sweat at night for very simple reasons, like having too much or too less clothes on. If they are cold, they should have a cold nose. It is therefore very important to check the clothing and keep the room temperature pleasant.