37.6 - 38.4 deg C seems fine... The fever is trending down, from its peak at 39.4 deg C.
If doctor says he's ok and your boy is happy the day, then relax.
Just keep him well hydrated and sponge him with warm water regularly.
Your boy's body is probably fighting a virus new to his body and having a slight fever is nature's way of protecting the body.
Read Fever in Children Causes, Symptoms and Treatment by eMedicineHealth.com