  Critical properties of the compact three-dimensional U(1) lattice gauge
theory are explored at finite temperatures. The critical point of the
deconfinement phase transition, critical indices and the string tension are
studied numerically on lattices with temporal extension N_t = 8 and spatial
extension ranging from L = 32 to L = 256. The critical indices, which govern
the behaviour across the deconfinement phase transition, are generally expected
to coincide with the critical indices of the two-dimensional XY model. It is
found that the determination of the infinite volume critical point differs from
the pseudo-critical coupling at L = 32, found earlier in the literature and
implicitly assumed as the onset value of the deconfined phase. The critical
index $\nu$ computed from the scaling of the pseudocritical couplings agrees
well with the value $\nu$ = 1/2 of the XY model. The computation of the index
$\eta$ brings to a value larger than expected. The possible reasons for such
behaviour are discussed.
