Rotational diagrams of the ¹²CO v = 1−0 transitions. On the left is a simulation of the S CrA N CRIRES+ data with the spectral resolution and wavelength coverage of JWST MIRI-MRS, which does not have the resolution to distinguish between different kinematic components and only covers high-J lines. Three optically thin models with different temperatures are shown for illustration. The 4700 K is the best linear fit result. On the right is what is observed with VLT-CRIRES+. Only detected transitions are shown. The lines correspond to a linear fit to the simulated MIRI data (left) and the best-fit LTE model to the CRIRES+ data (right). In order to constrain the gas temperature and column density, sufficient upper energy level coverage is needed. In the right panel, we provide the coverage of two M-band filters of CRIRES+ (black) that provide sufficient to characterize the CO gas. The coverage of one of the oCRIRES filters is shown in grey. The upgrades to CRIRES+ result in greater energy level coverage with a single filter. The two model lines correspond to the P- and R-branch lines.