The heat outputs of higher burn up spent fuels (SF) create problems for disposal in mined repositories, including needs for reduced container loadings and extended pre-disposal cooling. An alternative that is less temperature sensitive is deep borehole disposal (DBD) which offers safety, cost, security and other potential benefits and could be implemented relatively quickly using currently available deep-drilling technology. We have modified our previously proposed version of DBD to be more appropriate for higher burn-up fuels by using smaller (0.36 m diameter) stainless steel containers, a smaller (0.56 m diameter) borehole, and different support matrices. We present the results of new heat-flow modelling for DBD of UO2 and MOX SF with burn ups of 55 and 65 GWd/t showing how temperatures evolve, especially on the outer surface of the containers. Consequences for the performance of the support matrices and the disposal concept are discussed. The thermal modelling indicates DBD is a viable option for higher burn-up SF and could be a practical disposal route for many combinations of fuel types, burn ups, ages and container loadings. Further, the results suggest that DBD of complete fuel assemblies, a desirable option, would be feasible and require much shorter pre-disposal cooling than necessary for disposal in mined repositories.