October is the obvious answer — Oktoberfest runs for 18 days in the second and third weeks of the month, drawing over a million visitors and transforming the city. If you want to experience it, be aware that accommodation books out months in advance and prices multiply. The festival is genuinely spectacular and worth the effort, but it requires planning.
The rest of the year Blumenau is pleasant and uncrowded. The subtropical climate means it is warm year-round, with summer (December to February) being hot and humid and prone to heavy rain. The famous 2008 flood hit in November; the surrounding hill slopes are prone to landslides in heavy rain years. Autumn (March to May) and spring (August to October, excluding festival time) offer the most comfortable conditions.