The floating ice tongue of the 79N Glacier in Northeast Greenland has been thinning over the past two decades, with warning signs of a potential onset of disintegration. While previous studies primarily attribute the thinning of the ice shelf to oceanic heat flux, limited attention has been given to the significant role of ice shelf plume dynamics as a mechanism for distributing the heat beneath the ice shelf. Here, we develop a horizontal two‐dimensional plume model to assess the effects of key factors influencing plume dynamics and, consequently, the estimation of a high‐resolution basal melt rate. We examine the effect of ice basal topography roughness and the presence of basal channels, that is extreme roughness of the base in the hinge zone, as well as the impact and pathways of subglacial discharge on melt rates. Our model results show good agreement with observation‐based melt rate estimates and indicate that basal channels in the hinge zone are the dominant control on the ice shelf's basal melt rates. In combination with subglacial discharge, the melt rate is increased to at the grounding line, intensifying the channelized melt rate pattern created by basal channels and increasing spatial variability. Additionally, our results indicate that incorporating wet‐dry algorithms and calculating a variable drag coefficient are crucial for accurately estimating melt rates during low subglacial discharge season, as well as for determining friction and turbulent exchange coefficients.