My husband is burning up with a fever and he says that he's cold, could it be the flu?

Yes.

Could be other illnesses too. Could be a large number of illnesses.

Thermal dynamics and body temperature lesson. When you touch something it will either feel warm or cold. If it is warm, then energy is flowing from the object to your hand. If it is cold then energy is flowing from your hand to the object. If it is kind of neutral then there isn't much of any energy flowing.

If you're feverish that means that your body temperature is greater then normal. Everything you normally touch will feel colder because the energy is flowing from his body to the environment.

The best course of action is to go to a doctor and get treatment. Most clinics have the face masks, especially in my region, so use one of those, but see about getting treatment.