After a gruelling three or so minute search revealed no hits for this idea, an hb search shows that kudos go to [Bigsleep] for an anno to Un-Brella2.
"For summer there's the Fresnel lens umbrella.
bigsleep, Jan 14 2014"
During the dog days of summer, heat of focussed light from a Fresnel Umbra-lens
could be used to generate coolth using an Einstein Szilard patent for a compressor-less refrigerator elongated and contained within the handle.
Since the light has been bent, the user should remain shaded even though the umbrella is clear.
During rainy days disable refrigeration. Focussed uv rays would still heat the absorbtive portion of the shaft and the inner surface of the parabolic canopy would redirect the rising heat back onto the holder.