Viral Exanthem: This is a common cause of a macular rash on the torso, especially in the absence of systemic symptoms like fever or itching. Viral exanthems are often self-limiting and can be caused by a variety of viruses.

Contact Dermatitis: This could be a likely diagnosis if the patient has been exposed to a new substance or product that came into contact with the torso. The lack of itching might make this less likely, but some forms of contact dermatitis can present without pruritus.
Pityriasis Rosea: Characterized by a herald patch followed by a secondary eruption of oval-shaped, scaling patches, pityriasis rosea often starts on the torso. The absence of scaling and the description of the rash as macular might make this less likely, but it remains a consideration.
Tinea Corporis (Ringworm): Although typically pruritic and with a more distinct border, some cases of tinea corporis can present with minimal symptoms and a macular appearance, especially in the early stages.

Meningococcemia: Although rare and typically associated with more severe symptoms like fever and shock, meningococcemia can present with a rash. The rash can be macular or petechial and is a medical emergency. The absence of fever does not rule out this diagnosis entirely.
Endocarditis: In rare cases, endocarditis can present with a rash (e.g., Janeway lesions), which might be macular. The lack of other symptoms like fever or heart murmurs makes this less likely, but it's a diagnosis that could have severe consequences if missed.
Lymphoma: Certain types of lymphoma, like cutaneous T-cell lymphoma (e.g., mycosis fungoides), can present with skin manifestations that might initially appear as a benign macular rash. This diagnosis is critical to consider due to its potential severity and the need for early intervention.

Erythema Migrans (Lyme Disease): Typically presents as a single, expanding lesion, but in rare cases, multiple lesions can occur. The rash is often described as having a "bull's-eye" appearance but can be macular in the early stages.
Secondary Syphilis: Can cause a wide variety of skin rashes, including macular types. The rash of secondary syphilis is often accompanied by other symptoms like lymphadenopathy and mucocutaneous lesions, but these might not always be present.