Jaén is at its best in spring (March-May) and autumn (September-November), when temperatures sit between 15 and 25°C and the surrounding olive country is at its most photogenic — flowering wildflowers in spring, mature trees heavy with fruit in autumn.
Summer (June-August) is brutal. Temperatures regularly hit 38-40°C; the city empties out at lunch and revives only after dark. Visit if you must, but stick to mornings and evenings.
Winter is cool and clear — the castle hill gets the occasional dusting of snow but daytime temperatures are 8-15°C. The Fiesta de la Virgen de la Capilla (10-11 June) and Semana Santa (Holy Week, the week before Easter) are the two big events worth timing a trip around.
The olive harvest, November to February, is when the surrounding countryside is at its busiest — visit a mill in production if you can.