Temps in baby

So my DS has been cranky all day but i kept taking his temp and it was in the 98 range...well bedtime struck and he absolutely was a terror..screaming and crying and just not a normal night for us...so we finally got him to sleep and he just woke up out of no where screaming at the top of his lungs...got him calmed down and noticed he felt a littlw cool so i took his temp again which i did under the arm cuz he was finally sleeping, and it said 96.2...is this normal????