We consider a system of thermoelastic plates with the same conductivity. The coupling in each plate component involves the average temperature of all the plates in the system. We show that if the coefficients of flexural rigidity are pairwise distinct, then the system underlying semigroup is exponentially stable. This is done first for the Fourier model, and then for the Maxwell–Cattaneo model. In particular, for the Maxwell–Cattaneo model, exponential stability is established when the rotational inertia is accounted for, while only polynomial stability is established otherwise. We use a combination of the multiplier techniques and the frequency domain method to prove all results.