Viral Exanthem: This is the most common cause of a papular rash with fever in both children and adults. Viral exanthems are rashes caused by viral infections, and they can be associated with a variety of viruses, including but not limited to, enteroviruses, adenoviruses, and parvovirus B19. The justification for this being the single most likely diagnosis is the high prevalence of viral infections in the population and the common presentation of a rash with fever.

Allergic Contact Dermatitis: This condition occurs when the skin comes into contact with an allergen, causing an immune reaction that leads to a rash. It's likely because many substances can cause allergic reactions, and the presentation can sometimes mimic a viral exanthem, especially if the allergen exposure is widespread.
Drug Rash: Also known as drug eruption, this is a reaction to a medication that can cause a variety of skin manifestations, including a papular rash. It's a likely diagnosis because many drugs can cause rashes, and the history of recent medication use is a critical part of the diagnostic workup.
Insect Bite Reaction: Reactions to insect bites can cause papular rashes and can be accompanied by fever, especially if there is a significant allergic reaction or if the bites become infected. This is a common occurrence, especially during certain times of the year or in specific geographic locations.

Meningococcemia: This is a severe infection caused by Neisseria meningitidis that can present with a rash and fever. It's critical not to miss this diagnosis because meningococcemia can rapidly progress to sepsis and death if not promptly treated with antibiotics.
Rocky Mountain Spotted Fever (RMSF): Caused by Rickettsia rickettsii, RMSF is a tick-borne illness that can present with fever and a rash. It's a "do not miss" diagnosis because delayed treatment can lead to severe complications and death.
Stevens-Johnson Syndrome/Toxic Epidermal Necrolysis (SJS/TEN): These are severe skin conditions usually triggered by medications or infections, characterized by widespread skin necrosis and detachment. They are life-threatening and require immediate medical attention.

Kawasaki Disease: An acute febrile illness of childhood characterized by inflammation in the walls of medium-sized arteries throughout the body, which can present with a rash and fever. It's rare but important to consider in children because of its potential to cause coronary artery aneurysms if not treated.
Erythema Multiforme: A skin condition characterized by target lesions, which can be triggered by infections or medications. While not as common as other rashes, it has a distinctive appearance and can be associated with significant morbidity if not recognized and managed appropriately.
Secondary Syphilis: Can present with a variety of skin manifestations, including a papular rash, and is accompanied by fever. It's a rare diagnosis in the context of a random distributed papular rash but should be considered, especially in individuals with high-risk sexual behavior or exposure history.