Your son most likely has a simple rash or irritation on the tip of his penis that is causing the burning sensation.
Because you say that your 8 year old son still feels the burning sensation after peeing in his diaper, then it's likely irritation.
Try examining his penis to see if it looks a bit red or even somewhat purple.
My 6 year old son who wets the bed and wears diapers had the same issue and it turned out that it was just irritation from the diaper and pee, even though he would clean up.
If possible, I would allow him to air out for a few hours at a time before putting another diaper on or let him go all day without a diaper and just change his pants for awhile, if he pees in them.
If the pee burning last longer than a few days, it could be a UTI, but if he's not peeing any blood, it's most likely just irritation, but just keep an eye out and if it continues to burn, take him to the doctor or urgent care.