By mid-century, climate change is expected to push millions of migrants across borders, yet direct empirical evidence is limited. Using recent monthly bilateral flow data for 127 developing-country origins and 180 destinations, we estimate migration responses to weather shocks. High-dimensional fixed-effects absorb all origin-, destination-, and migration corridor-by-year confounders, seasonality, and global shocks; identification exploits residual within-corridor weather anomalies. We find no evidence that climate stress raises emigration: higher origin temperatures reduce outflows, while precipitation has no effect. Complementary analysis pinpoints depressed origin income as an underlying mechanism: climate stress tightens household budgets, decreasing the financial viability of international movement.