Spring (March to May) and autumn (September to November) are the best times to visit: temperatures are comfortable for walking the old city and security conditions are generally calmer around major religious holidays. Summer is hot — Hebron sits at around 900 metres elevation, which moderates the heat somewhat compared to the coastal plain, but July and August are still warm. Winter is mild by day but can be cold at night.
Be aware of Jewish and Muslim holidays when planning a visit. The Cave of the Patriarchs is divided and access rules are modified around ten Jewish holidays a year when the entire building is given over to Jewish prayer; on ten other days, the entire building is given over to Muslim prayer. The holiday schedule is published in advance and is worth checking if visiting the cave is your primary reason for coming.