Near-field radiation allows heat to propagate across a small vacuum gap at rates several orders of magnitude above that of far-field, blackbody radiation. Although heat transfer via near-field effects has been discussed for many years, experimental verification of this theory has been very limited. We have measured the heat transfer between two macroscopic sapphire plates, finding an increase in agreement with expectations from theory. These experiments, conducted near 300 K, have measured the heat transfer as a function of separation over mm to μm and as a function of temperature differences between 2.5 and 30 K. The experiments demonstrate that evanescence can be put to work to transfer heat from an object without actually touching it.