What is the benefit of fever during infections?
Fever is a trait observed in warm and cold-blooded vertebrates that has been conserved for hundreds of millions of years (Evans, 2015). 

Elevated body temperature stimulates the body's immune response against infectious viruses and bacteria. It also makes the body less favorable as a host for replicating viruses and bacteria, which are temperature sensitive (Source: Sci Am). 

The innate system is stimulated by increasing the recruitment, activation and bacteriolytic activity of neutrophils. Likewise, natural killer cells' cytotoxic activity is enhanced and their recruitment is increased, including that to tumors. Macrophages and dendritic cells increase their activity in clearing up the mess associated with infection.

Also the adaptive immune response is enhanced by elevated temperatures. For example, the circulation of T cells to the lymph nodes is increased and their proliferation is stimulated.

In fact, taking pain killers that reduce fever have been shown to lead to poorer clearance of pathogens from the body (Evans, 2015). In adults, when body temperature reaches 104 oF (40 oC) it can become dangerous and fever reducing agents like aspirin are recommended (source: eMedicine) 

Reference
- Evans, Nat Rev Immunol (2015); 15(6): 335–49