Aims:I deduced a 3D sunspot model that is in full agreement with spectropolarimetric observations, in order to address the question of a possible penumbral heating process by the repetitive rise of hot flow channels. Methods: I performed inversions of spectropolarimetric data taken simultaneously in infrared (1.5 μm) and visible (630 nm) spectral lines. I used two independent magnetic components inside each pixel to reproduce the irregular Stokes profiles in the penumbra and studied the averaged and individual properties of the two components. By integrating the field inclination to the surface, I developed a 3D model of the spot from inversion results without intrinsic height information. Results: I find that the Evershed flow is harbored by the weaker of the two field components. This component forms flow channels that show upstreams in the inner and mid penumbra, continue almost horizontally as slightly elevated loops throughout the penumbra, and finally bend down in the outer penumbra. I find several examples where two or more flow channels are found along a radial cut from the umbra to the outer boundary of the spot. Conclusions: I find that a model of horizontal flow channels in a static background field is in good agreement with the observed spectra. The properties of the flow channels correspond very well to the moving tube simulations of Schlichenmaier et al. (1998, A&A, 337, 897). From the temporal evolution in intensity images and the properties of the flow channels in the inversion, I conclude that interchange convection of rising hot flux tubes in a thick penumbra still seems a possible mechanism for maintaining the penumbral energy balance.