May, June, and September are the best months — warm enough for the beach, not brutally hot, and significantly less crowded than July and August. July and August are peak season: temperatures regularly exceed 35°C, the museums and Knossos are packed with tour groups, and flights and accommodation prices are at their highest.
Spring (April–May) is particularly pleasant: the hills south of the city are green, wildflowers are out, and the archaeological sites are uncrowded. The Peza wine region holds its harvest festival in late September, a good time to visit the wineries.
Iraklion works fine as a winter destination for a museum-focused visit. The Archaeological Museum is open year-round and far better in winter than in the summer scrum. Temperatures rarely drop below 10°C.