Planck's law predicts the distribution of radiation energy, color and intensity, emitted from a hot object at thermal equilibrium. The Law also sets the upper limit of radiation intensity, the blackbody limit. Recent experiments reveal that micro-structured tungsten can exhibit significant deviation from the blackbody spectrum. However, whether thermal radiation with weak non-equilibrium pumping can exceed the blackbody limit in the far field remains un-answered experimentally. Here, we compare thermal radiation from a micro-cavity/tungsten photonic crystal (W-PC) and a blackbody, which are both measured from the same sample and also in-situ. We show that thermal radiation can exceed the blackbody limit by >8 times at λ = 1.7 μm resonant wavelength in the far-field. Our observation is consistent with a recent calculation by Wang and John performed for a 2D W-PC filament. This finding is attributed to non-equilibrium excitation of localized surface plasmon resonances coupled to nonlinear oscillators and the propagation of the electromagnetic waves through non-linear Bloch waves of the W-PC structure. This discovery could help create super-intense narrow band thermal light sources and even an infrared emitter with a laser-like input-output characteristic.