  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.
