Three-dimensional compact U(1) LGT is studied at finite temperature. For small values of the spatial gauge coupling one obtains an effective two-dimensional spin model which describes interaction between the Polyakov loops of the original theory. The effictive model is studied in some limiting cases. Correlation functions of the Polyakov loops and the 't Hooft operator are computed perturbatively at high temperatures. Performing dimensional reduction the two-dimensional Coulomb gas like-model is calculated which is then used to reveal some properties of vortex--anti-vortex configurations in the high-temperature regime and allows to compute critical indices. Our results are consistent with the conjecture that the finite-temperature U(1) LGT belongs to the universality class of the two-dimensional XY model.