  We consider the phase structure of a pure compact U(1) gauge theory in four
dimensions at finite temperature by treating this system as a perturbative
deformation of the topological model. Phases of a gauge theory can be
investigated from the phase structure of the topological model. The thermal
pressure of the topological model has been calculated, from which its phase
structure can be derived. We have obtained phases of a compact U(1) gauge
theory. Moreover, the critical-line equation has been explicitly evaluated.
