Near-field thermal emission can be engineered by using periodic arrays of subwavelength emitters. The array thermal emission is dependent on the shape, size, and material properties of the individual elements as well as the period of the array. Designing periodic arrays with desired properties requires models that relate the array geometry and material properties to the near-field thermal emission. In this study, a periodic method is presented for modeling two-dimensional periodic arrays of subwavelength emitters. This technique only requires discretizing one period of the array, and thus is computationally beneficial. In this method, the energy density emitted by the array is expressed in terms of the array's Green's functions. The array Green's functions are found using the discrete dipole approximation in a periodic manner by expressing a single point source as a series of periodic arrays of phase-shifted point sources. The presented method can be employed for modeling periodic arrays made of inhomogeneous and complex-shape emitters with nonuniform temperature distribution. The proposed technique is verified against the nonperiodic thermal discrete-dipole-approximation simulations, and it is demonstrated that this method can serve as a versatile and reliable tool for studying near-field thermal emission by periodic arrays.