Abstract: A mathematical model describing the in-mold temperature contour for a GCr15 rectangular bloom was determined using FEM. Temperature-dependent thermophysical parameters along with average heat flow, transient heat flow, and corner air gap in boundary conditions were used to study temperature contour and billet shell thickness of rectangular blooms under different boundary conditions. Simulation experiments indicated that the temperature range with an average heat flow boundary was wider than that with transient heat flow when not considering the air gap. With the air gap, however, the ranges were similar. Corner air gap only affected the temperature of the corner region, while the core, wide face center, and narrow face center regions were not affected. Corner shell thickness with an air gap was 6 to 7 mm narrower than the one without air gap, and the hot spot area appeared 30 mm away from the corner.