We study the influence of thermal fluctuations in the phase diagram of a recently introduced two-dimensional phase field crystal model with an external pinning potential. The model provides a continuum description of pinned lattice systems allowing for both elastic deformations and topological defects. We introduce a non-conserved version of the model and determine the ground-state phase diagram as a function of lattice mismatch and strength of the pinning potential. Monte Carlo simulations are

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... used to determine the phase diagram as a function of temperature near commensurate phases. The results show a rich phase diagram with commensurate, incommensurate and liquid-like phases with a topology strongly dependent on the type of ordered structure. A finite-size scaling analysis of the melting transition for the c(2 × 2) commensurate phase shows that the thermal correlation length exponent ν and specific heat behavior are consistent with the Ising universality class as expected from analytical arguments.