Gastroenteritis: This is often the first consideration for vomiting, even without fever, as it can be caused by viral infections that may not always present with fever. The duration of one week could indicate a viral cause that is taking time to resolve.

Food Poisoning: Although typically associated with a shorter duration, some forms of food poisoning can cause prolonged vomiting without fever, depending on the causative agent.
Gastroesophageal Reflux Disease (GERD): GERD can cause chronic vomiting, especially after eating, and does not typically present with fever.
Psychogenic Vomiting: This can be a consideration, especially if the vomiting is associated with stress, anxiety, or other psychological factors, and there's no clear gastrointestinal cause found.

Appendicitis: Although classically presents with abdominal pain, nausea, vomiting, and fever, some cases may not have fever, especially in the early stages or in certain populations like the elderly or young children.
Intestinal Obstruction: This is a surgical emergency that can present with vomiting, abdominal pain, and constipation, without fever. Early diagnosis is crucial to prevent complications.
Pancreatitis: Can cause severe vomiting and abdominal pain, and while fever may not always be present, it's a critical diagnosis to consider due to its potential severity.

Cyclic Vomiting Syndrome: A rare condition characterized by recurrent episodes of severe vomiting lasting hours to days, with periods of normal health in between. It does not typically present with fever.
Increased Intracranial Pressure: Rarely, increased intracranial pressure (e.g., due to a brain tumor) can cause vomiting without fever, often accompanied by other neurological symptoms like headache or visual disturbances.
Addison's Disease: A rare endocrine disorder that can cause vomiting among other symptoms like fatigue, weight loss, and changes in skin pigmentation, without fever.