I would not advise cycling when you get a fever or a cold. I know whenever I am down with fever and visit a doctor, what they would suggest is that you keep yourself low, be in bed, and drink a lot of water and teas, no stress, no walking, no cycling, no going out if it is cold, just stay low and keep yourself warm. A good intake of vitamins, fluit and vegetable is advised, too.
I am afraid you could make it worse if you go on a ride with a fever. Try to get rid of it, cure yourself, and make sure you can withstand cold wind on your face, throat and neck, because if you are sick, and you ride, you also sweat a lot, and being so cold outside, it is not good for your body, warm body exposed to cold wind...plus fever.
I would skip cycling if I were sick.