What Causes Low Body Temperature With Redness On Jawline?

My child, age 5, has a limb difference--his arm ends a few inches below the shoulder. He is prone to high fevers. A fever ran on and off from Tuesday to Saturday night together with a cough. A doctor checked him Friday and said antibiotics were not needed. Sunday his temp was low (97, his is usually 98.6 or so) Sunday night his temp dropped to 95.8. Tuesday he was up to 98.1. Tonight--Tuesday night--he is EXTREMELY IRRITABLE and is down to 96.5. We are measuring the temp with a Braun ear thermometer that seems to be working fine. We don't see any rashes, but his face may be a little red on his jawline. What could be causing this low temperature??