noun
BAD : I'd caught a cold and had a high fever.
GOOD : I'd caught a cold and had a high temperature.
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When someone feels rather ill and their body is hotter than usual, they have a (high) temperature : 'I feel as if I've got a temperature.' 'She's in bed with a high temperature.'
A fever usually refers to a (dangerously) high body temperature, or the disease that produces this: 'In the steaming jungle he had contracted a fever.' 'It seemed as if the fever would shake him to pieces.'