We describe the direct measurement of the expulsion of a magnetic field from a plasma driven by heat flow. Using a laser to heat a column of gas within an applied magnetic field, we isolate Nernst advection and show how it changes the field over a nanosecond timescale. Reconstruction of the magnetic field map from proton radiographs demonstrates that the field is advected by heat flow in advance of the plasma expansion with a velocity vN=(6±2)×105 m/s. Kinetic and extended magnetohydrodynamic simulations agree well in this regime due to the buildup of a magnetic transport barrier.