This study analyzed summer observations of diurnal and seasonal surface energy budgets across several monitoring sites within the Arctic tundra underlain by permafrost. In these areas, latent and sensible heat fluxes have comparable magnitudes, and ground heat flux enters the subsurface during short summer intervals of the growing period, leading to seasonal thaw. The maximum entropy production (MEP) model was tested as an input and parameter parsimonious model of surface heat fluxes for the simulation of energy budgets of these permafrost‐underlain environments. Using net radiation, surface temperature, and a single parameter characterizing the thermal inertia of the heat exchanging surface, the MEP model estimates latent, sensible, and ground heat fluxes that agree closely with observations at five sites for which detailed flux data are available. The MEP potential evapotranspiration model reproduces estimates of the Penman‐Monteith potential evapotranspiration model that requires at least five input meteorological variables (net radiation, ground heat flux, air temperature, air humidity, and wind speed) and empirical parameters of surface resistance. The potential and challenges of MEP model application in sparsely monitored areas of the Arctic are discussed, highlighting the need for accurate measurements and constraints of ground heat flux.