We explore the potential for changing sea ice thickness (SIT) in the Arctic to impact fossil resource extraction-driven shipping activities over the Northern Sea Route (NSR). Using the case study of oil extracted from Russian Arctic offshore reserves and shipped to East Asian markets, we compare projected costs of shipping over the NSR versus the Suez Canal Route (SCR). Our analysis incorporates impacts of climate change on the SIT-dependent cost of shipping on the NSR. We also leverage a MultiSector Dynamics model to incorporate impacts of both climate change and global climate change mitigation efforts on the SIT-dependent cost of producing Russian Arctic offshore oil and global demand for the oil. We find that the NSR will become increasingly cost-competitive with the SCR over the century, particularly in a higher warming scenario. As costs associated with the NSR decrease, shipping traffic, and associated CO₂ and particulate matter emissions, will increase along the NSR, with the spatial distribution of traffic and emissions depending on the magnitude of future warming. These insights could have implications for energy system transition decisions, global trade dynamics, and NSR port development strategies.