  We consider G\"odel temporal logic ($\sf GTL$), a variant of linear temporal
logic based on G\"odel--Dummett propositional logic. In recent work, we have
shown this logic to enjoy natural semantics both as a fuzzy logic and as a
superintuitionistic logic. Using semantical methods, the logic was shown to be
{\sc pspace}-complete. In this paper we provide a deductive calculus for $\sf
GTL$, and show this calculus to be sound and complete for the above-mentioned
semantics.
