> Would attaching a heat sink to my shed cool it below the ambient temperature?To which the answer is obviously no.
Except it's "yes" if you define "ambient temperature" as the temperature inside the shed on a sunny day, and if you put the radiating fins of the heatsink in the cooler outside air, which is the equivalent of what the paper does! You can criticize that this is a poor definition of ambient, but it is the one they use.
No configuration of heat sink + device will decrease the temperature unless we put some "work" into the system. That "work" will be electrical energy of some sort The source is irrelevant. It must be external to the system and it must have a cooling effect. We absolutely need some sort of peltier device (or other refrigeration technology). There is no way around it!
So when I take a shower and then and then see water condensing on the inside of my single pane bathroom window on a cold night, it means there's got to be a hidden Peltier cooler in there somewhere? Or in a more exact comparison, if I have an outdoor greenhouse on a cold but sunny day, and I see water condensing on the inside of the glazing, there's got to be a refrigerator making it happen? No, there just needs to be a temperature differential, and the heat sink acts like a cold window.
At 25C and 100% humidity air can hold about 0.02ml of water. Meaning for every one liter of water you need 50,000 liters of air.
By contrast, this is an appropriate criticism! Yeah, to collect a liter (1 kg) of water at 25C and 50% humidity, you'd need to extract all the water from 100,000 liters of air. And since you aren't going to get all the water out, you it probably needs to process several times that amount. Is this absurd? It probably depends on how much water you need. An Olympic Swimming Pool is 50m x 25m x 2m, so that amount air would give you something between 1 and 25 liters of water depending on your efficiency of extraction.
How do you get this much air over your collector? It looks like a medium bathroom fan (70 cubic feet per minute) seems to move a little over 100,000 liters per hour, so it could move this amount of air in a day. Alternatively, if you wanted to do it without power, you'd probably get more than this amount of air flow with a gentle breeze. Whether it's worth it would depend on how thirsty you are in that desert and what your other options are, but it's still a neat technique!