  Electromagnetic radiation is emitted during the whole course of a heavy-ion
collision and can escape from the collision zone without further interactions.
This makes it an ideal tool to study the properties of hot and dense QCD
matter. To model the space-time evolution of the collision at SIS energies a
coarse-graining approach is used to convert transport simulations into
meaningful temperatures and densities. These parameters serve as input for the
determination of the pertinent radiation of thermal dileptons based on an
in-medium $\rho$ spectral function that describes available spectra at
ultrarelativistic collision energies. The resulting excitation function of the
thermal excess radiation provides a baseline for future measurements by the
HADES and CBM experiments at GSI/FAIR, and experiments proposed at NICA and
J-PARC.
