We introduce a new modelling framework including the Fast Line Tracer (FLITS) to simulate infrared line emission spectra from protoplanetary discs. This paper focusses on the mid-IR spectral region between 9.7 and 40 μm for T Tauri stars. The generated spectra contain several tens of thousands of molecular emission lines of H₂O, OH, CO, CO₂, HCN, C₂H₂, H₂, and a few other molecules, as well as the forbidden atomic emission lines of S I, S II, S III, Si II, Fe II, Ne II, Ne III, Ar II, and Ar III. In contrast to previously published works, we do not treat the abundances of the molecules nor the temperature in the disc as free parameters, but use the complex results of detailed 2D PRODIMO disc models concerning gas and dust temperature structure, and molecular concentrations. FLITS computes the line emission spectra by ray tracing in an efficient, fast, and reliable way. The results are broadly consistent with R = 600 Spitzer/IRS observational data of T Tauri stars concerning line strengths, colour, and line ratios. In order to achieve that agreement, however, we need to assume either a high gas/dust mass ratio of order 1000, or the presence of illuminated disc walls at distances of a few au, for example, due to disc–planet interactions. These walls are irradiated and heated by the star which causes the molecules to emit strongly in the mid-IR. The molecules in the walls cannot be photodissociated easily by UV because of the large densities in the walls favouring their re-formation. Most observable molecular emission lines are found to be optically thick. An abundance analysis is hence not straightforward, and the results of simple slab models concerning molecular column densities can be misleading. We find that the difference between gas and dust temperatures in the disc surface is important for the line formation. The mid-IR emission features of different molecules probe the gas temperature at different depths in the disc, along the following sequence: OH (highest)–CO–H₂O and CO₂–HCN–C₂H₂ (deepest), just where these molecules start to become abundant. We briefly discuss the effects of C/O ratio and choice of chemical rate network on these results. Our analysis offers new ways to infer the chemical and temperature structure of T Tauri discs from future James Webb Space Telescope (JWST)/MIRI observations, and to possibly detect secondary illuminated disc walls based on their specific mid-IR molecular signature.