Let E⊂Rn+1 be a parabolic uniformly rectifiable set. We
prove that every bounded solution u to ∂tu−Δu=0,inRn+1∖E satisfies a Carleson measure
estimate condition. An important technical novelty of our work is that we
develop a corona domain approximation scheme for E in terms of regular
Lip(1/2,1) graph domains. This approximation scheme has an analogous elliptic
version which is an improvement of the known results in that setting