No, super cooling wouldn't be effective, but if you made a concentrating collector of, say 200:1 you'd need to cool them to keep them alive and the energy removed might be used to drive a steam turbine to generate even more electricity. More practically a concentrating collector could use higher cost high efficiency solar cells and the water cooling could be used for home heating and hot water. So, if you used, say, 30% cells and were then able to reclaim 30% of the waste energy for hot water and heating the net efficiency would be closer to 50%.
We're not too far away from the point where solar becomes pretty much the cheapest source of energy. If every home and building complex covered the roof with 20% cells you could generate just about all the energy the country needs without requiring any additional land. We are not quite at 20% for general consumer (low cost) just yet but we're not far off at 15%. There are demo units in the lab at over 43% with concepts that go up to about 60%.
There is little wonder that the oil/gas/coal industries are terrified of solar and that explains the huge investment they've made to politicians to keep them from pushing solar.
The single biggest downside to solar is the need to build energy storage systems as about 35-40% of energy consumed is consumed at night. The new Tesla home battery system, scaled up to about 50Kwhr of usable storage may well be a game changer in this regard.
Brian