Context. With a new generation of observational instruments largely dedicated to exoplanets (i.e. JWST, ELTs, PLATO, and Ariel) providing atmospheric spectra and mass and radius measurements for large exoplanet populations, the planetary models used to understand the findings are being put to the test.Aims. We seek to develop a new planetary model, the Heat Atmosphere Density Evolution Solver (HADES), which is the product of self-consistently coupling an atmosphere model and an interior model, and aim to compare its results to currently available findings.Methods. We conducted atmospheric calculations under radiative-convective equilibrium, while the interior is based on the most recent and validated ab initio equations of state. We pay particular attention to the atmosphere-interior link by ensuring a continuous thermal, gravity, and molecular mass profile between the two models.Results. We applied the model to the database of currently known exoplanets to characterise intrinsic thermal properties. In contrast to previous findings, we show that intrinsic temperatures (Tint) of 200–400 K – increasing with equilibrium temperature – are required to explain the observed radius inflation of hot Jupiters. In addition, we applied our model to perform ‘atmosphere-interior’ retrievals by Bayesian inference using observed spectra and measured parameters. This allows us to showcase the model using example applications, namely to WASP-39 b and 51 Eridani b. For the former, we show how the use of spectroscopic measurements can break degeneracies in the atmospheric metallicity (Z) and intrinsic temperature. We derive relatively high values of Z = 14.79−1.91+ 1.80 × solar and Tint = 297.39−16.9+8.95 K, which are necessary to explain the radius inflation and the chemical composition of WASP-39 b. With this example, we show th.e importance of using a self-consistent model with the radius being a constrained parameter of the model and of using the age of the host star to break radius and mass degeneracies. When applying our model to 51 Eridani b, we derive a planet mass Mp = 3.13−0.040.05 MJ and a core mass Mcore = 31.86+0.32−0.18 ME, suggesting a potential formation by core accretion combined with a ‘hot start’ scenario.Conclusions. We conclude that self-consistent atmosphere–interior models efficiently break degeneracies in the structure of both transiting and directly imaged exoplanets. Such tools have great potential to interpret current and future observations, thereby providing new insights into the formation and evolution of exoplanets.