run a fever
To have an abnormally high body temperature (a fever), which is indicative of or caused by illness; to have a fever. After my toddler was lethargic all day, I begin to worry that she was running a fever.
run a fever and run a temperature
to have a body temperature higher than normal; to have a fever. I ran a fever when I had the flu. The baby is running a temperature and is grouchy.
run a fever
Also, run a temperature. Suffer from a body temperature higher than normal, as in She was running a fever so I kept her home from school. These idioms use run in the sense of "cause to move," in this case upward. [Early 1900s]