The structure and mechanical properties of clay nanoparticles is a subject of growing interest because of their numerous applications in engineering. We present the results of molecular dynamics simulation for a single nanoplate of pyrophyllite - a 2:1 clay mineral consisting of two tetrahedral sheets of SiO4 and an intervening octahedral AlO6 sheet. Simulations were performed in the temperature interval from 5 to 750 K using the ionic-type potentials of Cygan et al. On this basis the temperature dependences of structural parameters, characterizing both tetrahedral and octahedral sheets as well as single lamella, have been studied. Two slightly different structures were observed in this wide temperature interval. The mechanical properties of the nanoplate were calculated from stress-strain diagrams, which have been obtained at relatively slow rates of deformation (for molecular simulations). Using different types of loading, we calculated the full elasticity tensor and estimated the influence of temperature on its components. We estimated also the bending and torsion stiffnesses of the nanoplate as specific characteristics of this type of particle. Because the nanoplate is atomically thin, a reasonable determination of the thickness is a nontrivial problem, both in the modeling of mechanical properties and in physical interpretation of the obtained data. We propose a procedure for its calculation.