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(349) Dembowska is a large, bright main-belt asteroid that has a fast rotation and an oblique spin axis. It might have experienced partial melting and differentiation. We constrain Dembowska's thermophysical properties, such as thermal inertia, roughness fraction, geometric albedo and effective diameter within 3s uncertainty of Gamma = 20(-7)(+12) Jm(-2) s(-0.5) K-1, fr = 0.25(-0.25)(+0.60), p(v) = 0.309(-0.038)(+0.026) and D-eff = 155.8(-6.2)(+7.5) km, by utilizing the advanced thermophysical model to analyse four sets of thermal infrared data obtained by the Infrared Astronomy Satellite (IRAS), AKARI, the Wide-field Infrared Survey Explorer (WISE) and the Subaru/Cooled Mid-Infrared Camera and Spectrometer (COMICS) at different epochs. In addition, by modelling the thermal light curve observed by WISE, we obtain the rotational phases of each data set. These rotationally resolved data do not reveal significant variations of thermal inertia and roughness across the surface, indicating that the surface of Dembowska should be covered by a dusty regolith layer with few rocks or boulders. Besides, the low thermal inertia of Dembowska shows no significant difference with other asteroids larger than 100 km, which indicates that the dynamical lives of these large asteroids are long enough to make their surfaces have sufficiently low thermal inertia. Furthermore, based on the derived surface thermophysical properties, as well as the known orbital and rotational parameters, we can simulate Dembowska's surface and subsurface temperatures throughout its orbital period. The surface temperature varies from similar to 40 to similar to 220 K, showing significant seasonal variation, whereas the subsurface temperature achieves equilibrium temperature about 120-160 K below a depth of 30-50 cm.