Obviously this paper seems to describe what Rossi has been calling his "Quark" device. From the scant description, it sounds like a quasi-gas/metal vapor discharge tube. Per the description, the sealed small diameter tube would have Ni electrodes on each end with a 1.5cm gap. When such a tube reaches its operating discharge temperature, the plasma inside the tube is a far different temperature than the envelope of the tube. Collisions of the ions and electrons with the wall of the tube transfer heat and create a colder layer around the inside of the tube. Think of a neon sign. The hot orange plasma may have an effective plasma temperature of >2000°C but the lead glass tube will soften in the range of 600°C and melt substantially by 800°C. Plasma temperature is best characterized by its spectrum, but it will not necessarily be Boltzmann distribution - it could have strong lines that contain most of the energy which will impart a particular color. In a linear tube the plasma will be hotter in the center and will fall off in temperature with radius as it approaches the envelope boundary. It sounds like from this paper that the tube is not glass since an emissivity of 0.9 is being ascribed to it. Likely it is a thin alumina tube. Note that alumina appears opaque, but it is really translucent, so measuring the spectrum is important. The surface area being used is 1 cm^2 with a length of 1.5cm suggesting that the tube OD is 2.1mm - pretty small. So, at high outer surface temperature, if the spectrum shows a Boltzmann distribution, a blackbody calculation could be used for emitted power. In this case, the spectrum is only measured to 1.1 microns.
From their measurements, they estimate a temperature of the device surface at 2636°K or 2363°C. Alumina would melt at 2072°C, so either the tube is not alumina, or the tube surface temperature is wrong. It is likely that the tube is alumina and the tube surface temperature is wrong. As I mentioned, the tube can be much cooler than the plasma (for example the much cooler glass temperature of a neon sign), particularly if the tube is transparent. Alumina is translucent at visible and near infrared wavelengths - it has a high degree of transparency because its crystallites are randomly oriented sapphire. So it has scattering, but a high degree of transparency. This means that the diameter for the Boltzmann calculation would have to be some kind of average plasma discharge diameter inside the tube because it is not the tube surface that is at that temperature and radiating at the 2363°C Boltzmann spectrum - it is the inner plasma.
So, lets make an guess-timate for the diameter of the plasma. Lets say that the OD of the tube is 2.1mm, the ID of the tube might be 1.1mm. The diameter of the average emitting plasma discharge might be 0.4mm (just to guess). This would make the emitting area (0.4/2.1)x(1cm^2) = 0.19 cm^2 and would reduce the calculated output power to 47 watts. But, this estimate is prone to huge inaccuracy. What is needed is to measure the tube in a calorimeter. If you are going to do it optically, at least make a bolometric measurement of the emitted power/cm^2 and integrate over the sphere.
Once again, we see that Rossi could be fooling himself with poor measurements. That doesn't mean that he does not have excess power. It suggests we don't know how much he has if any due to poor measurements.