Measurements of heat transport at the transition from perfect thermal super-conductivity to nonlinear heat diffusion in pure 4He provide a very sensitive probe of matter wave coherence. Superfluid heat transport is proportional to the product of the superfluid density and the superfluid velocity, which are both directly related to the superfluid order parameter. From dynamic scaling theory, the correlation length near the superfluid transition provides a measure of the length over which phase fluctuations of the order parameter persist. Our measurements suggest that both the hydrostatic pressure variation within the liquid helium column, together with the heat flux Q, limit the otherwise divergent correlation length near the superfluid transition. Future measurements planned for the microgravity laboratory will provide the first extensive experimental test of a renormalized, field theoretic description of heat transport near the superfluid transition. It will also provide a conclusive experimental study of the influence of hydrostatic pressure effects and dynamical effects on the correlation length. A new class of microgravity experiments is proposed that will permit measurements to within 10 pK of the superfluid transition temperature, allowing an entirely new class of ultra-accurate scientific investigations to be performed.