The most spectacular time to visit Kumbum is during the Butter Festival in the first month of the Tibetan lunar calendar (usually February or early March), when elaborate yak-butter sculptures are displayed for a single ceremonial night. The fourth-month ceremony (May or June) is also a major event with philosophical debates and the display of a large outdoor thangka.
Summer months (June to August) see the most Chinese domestic tourists. Visiting on a weekday outside of the major ceremony periods gives you the monastery in something closer to its normal daily rhythm — monks going about their studies and prayers, incense smoke drifting through the courtyards, pilgrims doing circumambulations of the main halls. This is the version of Kumbum that stays with you.