  The inclination or $\lambda$-Lemma is a fundamental tool in finite
dimensional hyperbolic dynamics. In contrast to finite dimension, we consider
the forward semi-flow on the loop space of a closed Riemannian manifold $M$
provided by the heat flow. The main result is a backward $\lambda$-Lemma for
the heat flow near a hyperbolic fixed point $x$. There are the following
novelties. Firstly, infinite versus finite dimension. Secondly, semi-flow
versus flow. Thirdly, suitable adaption provides a new proof in the finite
dimensional case. Fourthly and a priori most surprisingly, our $\lambda$-Lemma
moves the given disk transversal to the unstable manifold backward in time,
although there is no backward flow. As a first application we propose a new
method to calculate the Conley homotopy index of $x$.
