  We study the existence and small scale behaviour of almost splitting maps
along a Ricci flow satisfying Type I curvature bounds. These are special
solutions of the heat equation that serve as parabolic analogues of harmonic
almost splitting maps, which have proven to be an indespensable tool in the
study of the structure of the singular set of non-collapsed Ricci limit spaces.
  In this paper, motivated by the recent work of Cheeger-Jiang-Naber in the
Ricci limit setting, we construct sharp splitting maps on Ricci flows that are
almost selfsimilar, and then investigate their small scale behaviour. We show
that, modulo linear transformations, an almost splitting map at a large scale
remains a splitting map even at smaller scales, provided that the Ricci flow
remains sufficiently self-similar. Allowing these linear transformations means
that a priori an almost splitting map might degenerate at small scales.
However, we show that under an additional summability hypothesis such
degeneration doesn't occur.
