We propose a forward modeling approach of coronal funnels to investigate the outer layers of the solar atmosphere with respect to their thermodynamical properties and resulting emission line spectra. We investigate the plasma flow out of funnels with a new 2D MHD time dependent model including the solar atmosphere all the way from the chromosphere to the corona. The plasma in the funnel is treated in the single-fluid MHD approximation including radiative losses, anisotropic thermal conduction, and two different parameterized heating functions. We obtain plasma properties ( e. g. density, temperature and flow speed) within the funnel for each heating function. From the results of the MHD calculation we derive spectral profiles of a low corona emission line (Ne VIII, 770 angstrom). This allows us e.g. to study the Doppler shifts, across the funnel. These results indicate a systematic variation of the Doppler shifts in lines formed in the low corona depending on the heating function used. The line shift above the magnetic field concentration in the network is stronger than in the inter-network in both cases. However, for one of the heating functions, the maximum blue-shift ( outflow) is not to be found in the very center of the funnel but in the vicinity of the center. This is not the case of the second heating function where the maximum is well aligned with the centre of the funnel. This model directly relates for the first time the form of the heating function to the thermodynamic and spectral properties of the plasma in a funnel.