Ephesus is open year-round, but the timing of your visit matters more here than almost anywhere else in Turkey. The site is almost entirely unshaded and exposed to the Aegean sun, and summer heat makes a visit between 10am and 4pm genuinely unpleasant and potentially dangerous. Spring (April–June) and autumn (September–October) are ideal — mild temperatures, good light, and fewer cruise ship groups.
July and August bring both the worst heat and the largest crowds. Cruise ships dock at Kuşadası a few kilometres away and disgorge hundreds of visitors at once. If you visit in summer, arrive before 8am when the gates open — you will have the site to yourself for about an hour before the groups arrive. Late afternoon, after 4pm, is also quieter. March and November are worth considering: cool, usually dry, rarely crowded, and the low light is excellent for photography.
The site is technically open in winter but some facilities may close and access to the Terrace Houses can be restricted after rain. The Ephesus Museum in Selçuk is a good wet-weather alternative and often less visited than the site itself.