The LEDs are simply attached to the inside back of the fixture housing, which acts as the heatsink.
That is actually the best you could do (as a lantern design engineer)
The housing has fins about 3/4" in height, spaced about 1/2" apart. That's it. The fixtures are surprisingly lightweight, so the metal housing must be quite thin.
The question is, what is the overall size of the fixture. I did my calculation assuming a 60cm width, 20cm height and negligible depth, just with about 2cm fins spaced about 30mm, whole body actiing as the heatsink.
Used
this calculator.
Redone the calculation using following data:
Length = 80mm (represents height of the fixture; fixed in the Demo, so scaled down the power instead)
Height = 40mm (represents the fin height; fixed in the demo; because twice of your description, halved the number of fins)
Width = 200mm (= width of the fixture corresponding to 1 LED module)
Base thickness = 5mm (maybe overestimated; had 10mm before, not much difference; represents the thickness of the fixture body material)
Number of fins = 8 (Because the fin height is fixed in the calculator as twice your value, divided the number by two; otherwise correspond to number of fins belonging to 1 LED)
Fin thickness = 8mm (Expect about half of that, made wider, to have similar thermal resistance to your fin height)
Source length = 20mm (correspond to the 80mm height instead of the full 200mm)
Source width = 50mm (assume the LED modulke is about 50x50mm size)
Heat power = 22W (corresponds to 170W total, reduced to the calculated section of the heat sink; =170W*80mm/200mm/3)
Ambient temperature = 30degC (hot evening just after sunset)
Emissivity = 80% (assume black paint)
No external airflow (just the one caused by the heat alone; quite pessimistic, could be only when under some roof or so)
And get
Tj = 66.5degC (here the Tj means module base temperature, as the internal heat resistances were neglected)
Lower temperature than before, because before I count less and smaller fins...
That does not sound like something wrong, actually spot on, where the LED's are rated (by sound quality manufacturers)
But what matters is really the overall fixture size...
For the ballast: I don't think the conditions are worse than with many HID's, only the ballast is simpler, so could be more efficient (I would expect about 95%; here the higher efficiency makes it cheaper - less problems with heatsinking).