The large vertical scale heights of the diffuse ionised gas (DIG) in disc galaxies are challenging to model, as hydrodynamical models including only thermal feedback seem to be unable to support gas at these heights. In this paper, we use a three dimensional Monte Carlo radiation transfer code to post-process disc simulations of the Simulating the Life-Cycle of Molecular Clouds (SILCC) project that include feedback by cosmic rays. We show that the more extended discs in simulations including cosmic ray feedback naturally lead to larger scale heights for the DIG which are more in line with observed scale heights. We also show that including a fiducial cosmic ray heating term in our model can help to increase the temperature as a function of disc scale height, but fails to reproduce observed DIG nitrogen and sulphur forbidden line intensities. We show that, to reproduce these line emissions, we require a heating mechanism that affects gas over a larger density range than is achieved by cosmic ray heating, which can be achieved by fine tuning the total luminosity of ionising sources to get an appropriate ionising spectrum as a function of scale height. This result sheds a new light on the relation between forbidden line emissions and temperature profiles for realistic DIG gas distributions.
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