This work investigates the effect of thermal property gradients on the edge cracking in a functionally graded coating (FGM coating) bonded to a homogeneous substrate subjected to a thermal shock. A closed-form, short time asymptotic solution of the temperature field in the FGM system is obtained using the Laplace transform and its asymptotic properties. Thermal stress intensity factors (TSIFs) are calculated for an edge crack in an Al 2 O 3 /Si 3 N 4 graded coating on a Si 3 N 4 substrate based on the asymptotic temperature solution. The numerical results show that the graded Al 2 O 3 /Si 3 N 4 coating has lower TSIFs and hence higher thermal fracture resistance compared with the homogeneous Al 2 O 3 coating.