Using a modified theory of integral operators it is possible to relate radially symmetric, time-dependent parabolic problems in a given number of dimensions to a similar problem in fewer dimensions. This allows to generalise results about analytic solutions, such as the domain of convergence, from the lower dimensional case. As a special case the heat equation is taken. Using the associated integral operator basic solutions can be constructed, which allow a scries development of an analytic solution, converging normally in a maximal radially symmetric domain.