Fuel channel flow blockage is a postulated accident scenario in graphite-moderated molten salt reactors (MSRs), caused by debris partially obstructing the flow in a hole inside a graphite moderator brick. This obstruction produces an increase in the fuel salt bulk temperatures in the blocked channel, resulting in a significant fraction of the deposited fission power being conducted through graphite from the blocked channel to the surrounding unblocked channels. In the blocked channel, a combination of forced convection and natural convection takes place, the latter being dominant at very strong flow rate reductions. At full blockage (with the fragment completely obstructing the flow), because of the poor thermal conductivity of fuel salt, correct estimation of the natural convection impact on heat transfer between the channel bulk and the walls is fundamental to determine whether boiling conditions are reached in the blocked channel. The proposed assessing approach, developed in collaboration with ThorCon in the frame of the ThorCon reactor core design and optimization, is presented in this work. Results from a case study based on the molten salt breeder reactor (MSBR) design and operating conditions are presented and discussed. These analyses show that with respect to full blockage accidents in other reactor types, the consequences of full channel blockage accidents in graphite-moderated MSRs are milder. For graphite-moderated MSRs, the main mechanical limits during the accident arise in thermal stresses in the graphite brick. Graphite thermal and mechanical properties, namely, bulk modulus, thermal expansion coefficient, ultimate strength, and thermal conductivity, are severely impacted by neutron irradiation through the life of the graphite. All these effects are taken into account in the current analysis and are discussed in the present work.