I'm running a fever/temperature.
I have a student who likes to ask where idioms come from. Since the meanings are not literal, it is challenging for her to remember them. It often helps her to attach a story or explanation to an idiom, even if it is only folk etymology.
I've not had any luck searching on EL&U or in any dictionary for the origins of the phrase. It's always present in dictionaries but for etymology just refers the reader to
run, which never explains the specific meaning in
running a fever/temperature.
If anyone knows where the phrase actually originates, it would be helpful, but even a non-referenceable* etymology would be useful.
*i.e. heard from some guy down the pub; learnt a long time ago but I forget where; made-up; etc.