  We consider the heat operator acting on differential forms on spaces with
complete and incomplete edge metrics. In the latter case we study the heat
operator of the Hodge Laplacian with algebraic boundary conditions at the edge
singularity. We establish the mapping properties of the heat operator,
recovering and extending the classical results from smooth manifolds and
conical spaces. The estimates, together with strong continuity of the heat
operator, yield short-time existence of solutions to certain semilinear
parabolic equations. Our discussion reviews and generalizes earlier work by
Jeffres and Loya.
