In giant planet atmosphere modelling, the intrinsic temperature T int and radiative-convective boundary (RCB) are important lower boundary conditions. Often in one-dimensional radiative-convective models and in three-dimensional general circulation models it is assumed that T int is similar to that of Jupiter itself, around 100 K, which yields a RCB around 1 kbar for hot Jupiters. In this work, we show that the inflated radii, and hence high specific entropy interiors (8-11 k b / baryon), of hot Jupiters suggest much higher T int . Assuming the effect is primarily due to current heating (rather than delayed cooling), we derive an equilibrium relation between T eq and T int , showing that the latter can take values as high as 700 K. In response, the RCB moves upward in the atmosphere. Using onedimensional radiative-convective atmosphere models, we find RCBs of only a few bars, rather than the kilobar typically supposed. This much shallower RCB has important implications for the atmospheric structure, vertical and horizontal circulation, interpretation of atmospheric spectra, and the effect of deep cold traps on cloud formation.