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Significant manifestations of adverse effects of climate change exist for crop agriculture throughout the developing world including Bangladesh. Despite wheat being the second most important staple food, any rigorous analysis of its sensitivity to climate change remains an unexplored area of research. This paper fills this gap by investigating wheat yield sensitivity to climate change over time and across climatic zones using 45-year district level panel data. Results revealed rising trends in average seasonal temperature and number of seasonal dry days and downward trends in planting and flowering stage rainfall. The rise in average temperature and number of dry days adversely affected wheat yield while greater planting and flowering stage rainfall has improved yield. Significant variations across regions and a positive trend over time were evident. The study's policy implications are explored in terms of the potential to expand wheat cultivation and its role in achieving SDG 2 regarding food security and SDG 6 concerning sustainable water management. Strengthening institutional support systems, market accessibility, science-driven climate change adaptations - including generation and dissemination of drought tolerant wheat varieties and enhancing farmers' capacity to switch from rice to wheat, constitute key areas of policy intervention critically important for achieving SDG 2 and SDG 6.