12 microwatts per 1 cm2
for an intuitive sense, it would take 125 hours to charge a standard phone with 1 sqM device
So the potential for the application you cite is whole watts of power, enough to recharge a phone or a lantern overnight. (though, at current silicon fabrication costs, the price would be prohibitive)
Thanks.
For 2W you need ~20m² (~200sqft). That is the size of two rooms. Probably using the surface of your whole roof you can get 4W or 5W.
5°C Delta T generation is pretty impressive though. There are some commercial systems that can operate with 60°C temperature Delta (organic rankine cycle) and recover about 12% of that energy.