  In this paper, we study the Poincar\'e compactification of the limiting
planar semiflow of a coupled PDE-ODE system composed by a reaction-diffusion
equation with large diffusion coupled with an ODE by a boundary condition in a
heating transition region. The nonlinear sources are nondissipative
polynomials. We guarantee conditions to apply the Invariant Manifold Theorem in
order to reduce the dimension of the PDE and we prove that the compactified
vector fields are close in the C1-norm. We give an example to present a
structurally stable problem without the global attractor.
