Loss of appetite during fever
The psychologic and behavioral components of sickness represent a highly organized strategy of the organism to fight infection. Sickness is generally accompanied by fatigue, numbness, coldness, muscle and joint aches, and reduced appetite. These symptoms are not simply an effect caused by the pathogen. Instead, it now believed to be an active defense strategy of the body, referred to as “sickness behavior”. Sickness behavior is thought to be an adaptive response that enhances recovery by conserving energy to combat acute inflammation (Maes et al. 2012). It is triggered by the proinflammatory cytokines produced by activated cells of the innate immune system due to the presence of pathogens. These cytokines include mainly interleukin (IL) 1 (IL-1α and IL-1β), IL-6, and tumor necrosis factor α (TNF-α) (Dantzer, 2009; Plata-Salamán, 1998).

One of the sickness behaviors is a loss of appetite. Among a host of other effects, cytokines are believed to inhibit feeding by their actions in the hypothalamus. The hypothalamus is an important neural center that regulates food intake (Plata-Salamán, 1998; Meister, 2000).  

I refer you to Maes et al (2012), Plata-Salamán (1998) and Dantzer (2009) for backgrounds and further reading, as cytokine immunology is highly complex and this answer is anything but complete. 

References
- Dantzer, Immunol Allergy Clin North Am (2009); 29(2): 247–64
- Maes et al, BMJ (2012); 10: 66
- Meister, Vitam Horm (2000); 59: 265-304
- Plata-Salamán, Semin Oncol (1998); 25(1 Suppl 1):64-72