Should you always give a child medicine to lower a mild fever?

No. In children, a fever (temperature above 100.4 f or 38 c) is usually an indication of an illness. Many doctors believe that fever is one of the ways the body fights off the infection. Fever activates the immune system and makes it harder for the infection to survive. My advice generally is to treat the child, not the fever. If he feels bad, treat. If not, don't. See a doctor if the fever persists.