From Longman Dictionary of Contemporary Englishhave a temperaturehave a temperature (also be running a temperature) to have a body temperature that is higher than normal, especially because you are sick Susie has a temperature and has gone to bed. → temperature
Examples from the Corpushave a temperature• For example, a beaker of water may have a temperature of 50°C but it does not have heat.• There was no improvement; she continued to have a temperature.• If you are feeling unwell, have a temperature or an infection, withdraw.• Scaled to size. dinosaurs would have temperatures reaching from 38.5 to 40.6°C. which would imply severe heat stress.