  We prove forward and backward parabolic boundary Harnack principles for
nonnegative solutions of the heat equation in the complements of thin parabolic
Lipschitz sets given as subgraphs $E=\{(x,t): x_{n-1}\leq
f(x'',t),x_n=0\}\subset \mathbb{R}^{n-1}\times\mathbb{R} $ for parabolically
Lipschitz functions $f$ on $\mathbb{R}^{n-2}\times\mathbb{R}$. We are motivated
by applications to parabolic free boundary problems with thin (i.e co-dimension
two) free boundaries. In particular, at the end of the paper we show how to
prove the spatial $C^{1,\alpha}$ regularity of the free boundary in the
parabolic Signorini problem.
