  We study the existence and regularity of solutions to the Cauchy problem for
the inhomogeneous heat equation on compact Riemannian manifolds with conical
singularities. We introduce weighted H\"older and Sobolev spaces with discrete
asymptotics and we prove existence and maximal regularity of solutions to the
Cauchy problem for the inhomogeneous heat equation, when the free term lies in
a weighted parabolic H\"older or Sobolev space with discrete asymptotics. This
generalizes a result previously obtained by Coriasco, Schrohe, and Seiler (Thm.
7.2 in Math. Z. 244 (2003), 235--269) by different means.
