At the Altitude Test Facility (ATF) of the University of Stuttgart a linear compressor cascade test rig serves the investigation of ice crystal icing (ICI) under engine realistic conditions. A numerical model of the first stage of NASA Stage 67 is validated with experimental data taken from literature and used to investigate the respective ice crystal icing conditions for prospective cascade experiments. Eleven operating points simulating climb conditions with constant non-dimensional power setting through ascending parcels of moist air are selected for analysis. Only the melting-dominated regime is considered. The 3D flow field is obtained using a RANS approach in combination with a Spalart-Allmaras one-equation turbulence model. The droplet and ice crystal trajectories are calculated based on an Eulerian framework. The computation of the surface energy balance is adapted from the Messinger model taking into account unsteady phenomena. Four of eleven selected operating points indicate the onset of substantial ice accretion. A static wet bulb temperature of freezing constitutes in general the lower icing limit for rig experiments. The upper icing limit depends on the ice water content impinging and sticking to the target surface.