Growing pains. Soak their feet in a nice hot/warm water for 15ish, wipe dry and put some soft socks or slippers. Its just growing. When i was young id cry and it hurt so it could be that.
Neuropathy is the most usual reason for burning discomfort. He should see a Dr.
I would just take him to Dr and then you will be sure and have peace of mind. All the best 
Restless leg syndrome.
I’m like that. Drives me crazy. My feet get hot when trying to sleep, I’ll wake up kicking. Fan on me every night of the year is the only way to sleep.
1 Like
Fact: Doctor. Don’t wait.
Have him checked for diabetes
GET HIM MEDICAL ATTENTION! He needs help not opinions and experiences of people in the internet!
Go to a chiropractor. Have him fully adjusted and it will go away.