run a temperature
To have an abnormally high body temperature (a fever), which is indicative of or caused by illness. Dan: "How's Pete feeling?" Marshall: "Well, he ran a temperature last night, but he seemed a lot better this morning after some rest." I think I've started running a temperature. Maybe I should go lie down.
have/run a ˈtemperature
have a higher body temperature than normal: She’s got a terrible headache and she’s running a temperature.