Occupied Camera Lighter

Does anything get cooler when a magnifying glass is focused on a surface?
Imagine an area Z with 2 concentric circles, the largest Y being the area of the glass, and the smaller X inner circle being the area where energy is focused. Most of the energy that hits the glass is focused on the smaller area. Without the glass, that energy would’ve struck the larger area. So, how much energy is in the part of the larger circle that the smaller circle doesn’t occupy, area W? Is this area cooler that the surrounding surface? Of course, energy diffusion takes place, so it gets some heat and light from surrounding space, but if area Z was viewed with a thermal imaging camera, what would the smaller areas look like?
If you’re confused as to which area is which, Z > Y, and Y = W+X
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