The town is at its most extraordinary during the Festival of San Francisco Javier in late September and early October — Mexican and Tohono O'odham pilgrims by the thousand fill the plaza, and the streets fill with music, food stalls, and dance. The peak is 4 October. A second, smaller pilgrimage in late May honours Padre Kino himself.
If you want to see the town without crowds, come in March or April for warm but not punishing weather. Summer (June through September) is genuinely hot — Sonoran desert temperatures regularly top 40°C. December and January are pleasant but the evenings cool quickly.