The best time to visit Turkestan is spring (April–May) or autumn (September–October). Summers are extremely hot on the southern Kazakh steppe, with temperatures regularly exceeding 40°C. Winters are cold but not as brutal as in northern Kazakhstan, though the steppe wind can be punishing.
Pilgrimage traffic is heaviest around Nowruz (the spring equinox, around 21 March) and during major Islamic holidays. If you want the mausoleum to yourself — or as close to it as you'll get — arrive on a weekday morning in spring or autumn before the tour buses from Shymkent arrive.