EN
The temperature induced roughening of the solid surface is described by means of a discrete Gaussian model, using integral operator technique. On the basis of the exact statistical identities, the formulae for several local moments, i.e. ⟨hi⟩), ⟨(hi)^{2}⟩ and ⟨hihj⟩ are derived. The results of computer calculations, including surface specific heat, are presented for three lattices with z = 3, 4, and 6. In discussion, some further applications of the presented method are suggested.