[en] Invariance under the five-parameter Schroedinger group of coordinate transformations is investigated in the context of the generalized heat equations usub(t)-kappausub(xx)+F(u,usub(x))=0. There are four classes of invariant equations, among them Burgers' equation and other nonlinear equations used in fluid dynamics. The Schroedinger invariance is explained by the fact that all invariant equations can be converted from the heat equation by simple transformations of u. A larger number of generalized heat equations is shown to be invariant if a more general concept of Schroedinger invariance is used and again they are simple conversions of the heat equation. The use of the Schroedinger group in the search for solutions to invariant equations is illustrated by two applications: first the similarity method is generalized to arbitrary one-parameter subgroups and ordinary differential equations are obtained for the invariant solutions, and then, Schroedinger transformations are applied to trivial solutions to produce new, non-trivial solutions. (Auth.)