Fever in very young babies is treated far more cautiously than in older children because their immune systems are immature and serious infections can develop quickly with few obvious signs. For this reason, a temperature of 38°C (100.4°F) or above in an infant under 3 months should always prompt a call to a doctor or a visit to urgent care without delay.
Do not give fever medicine to a young baby and simply wait to see what happens; the priority is to have a professional examine the baby and decide whether tests or treatment are needed. Watch also for poor feeding, unusual sleepiness, a weak or high-pitched cry, fewer wet nappies, or a baby who is unusually floppy or irritable.
For babies between 3 and 6 months, a fever should also be assessed promptly, especially if they seem unwell. Trust your instincts: if your baby seems different from usual, it is always reasonable to seek advice.