Well, I can reproduce some at least of Rossi's claims.
I take an arc lamp - for the sake of argument, a deuterium lamp - and its appropriate power supply.
I turn it on - after a brief warm-up, high power is temporarily supplied, and the arc is struck. After that, the arc is maintained by a relatively small current - tens to low hundreds mA.
From the subjective colour of that arc (NOT that I'm looking at t with the naked eye! - I value my eyesight), Wit's a bluish white. With spectrometry, and treating that arc as a black body, I can determine that its temperature, based on its peak spectral output, appears to be, yes, something over 7,000 K. (conventionally known as "cool white")
It gets better. If I (or a non-too-bright assistant) touches the quartz envelope of that lamp, there is badly burnt skin - it is very hot! It is not, however anything like as hot as the arc APPEARS to be, or the quartz would melt.
So far so good. I have a hot-looking arc, and a hot-feeling lamp, running on a low maintenance current
What I will NOT be able to do, however, is to confirm the "mathematical claim" of 22 kW heat output by heat flow measurements.
I could leave that lamp burning in a cold warehouse for as long as it lasted. No-one would begin to feel warm.
OTOH, I could ship in my domestic 24kW condensing gas-fired boiler, some pipes and radiators, and things would probably warm up a bit ( depending on warehouse dimensions, temperature differential between inside and outside, insulation, and draughtproofing.)
So far, so good. I, like Rossi have a hot arc (temperature calculated from known physics); the arc running at a few watts power measured; and a hot envelope around that arc.
This is where the problems begin. The arc must be in thermal equilibrium with its surroundings - it is burning steadily. The envelope containing that arc,is with, say 1 cm of the arc itself. Now, I think I'm right in saying that the most refractory transparent material known is fused quartz, which softens at c. 1680 deg C
Since the amp envelope is not turning to a molten blob, we know that the effective temperature of the whole device is less than 1680 deg C.
"Ah" you say. "But these devices are cooled - the heat is removed"
"Right!" I say. "But you can buy off the shelf an arc lamp with an arc of around the same temperature as Rossi's, calculated in the same way, and the only cooling is air-cooling, possibly fan-assisted. In no way can tens of kW of heat be removed"
So there's the challenge for Rossi-Replicators. Crowd fund whatever arc lamp and power supply you deem fit, and you will easily get an arc maintained by a few watts of power, which you will be able to show by Rossi's calculations to have a temperature of 6-8,000 K
Your challenge is to extract 22 kW heat from it, using whatever method of heat exchange you can find or invent.
Forza ragazzi!!