The first person credited with detecting heat from moonlight was Macedonio Melloni in 1846. Below is a brief description of the experiment from "Infrared metaphysics: the elusive ontology of radiation. Part 1" by Hasok Chang , Sabina Leonelli. (Btw, I have read elsewhere that the experiment was performed on top of Mount Vesuvius rather than on his apartment balcony. Scientific folklore perhaps?)
There is a link below of a video described as a reconstruction of Melloni's experiment. However it is only a laboratory demonstration using an electric burner as a source of infrared radiation, but it does use Melloni's large fresnel lens which is worth seeing. If the temperature change observed by Melloni was the same as in the video, then he observed an increase of only about 0.25 degrees. begin quote: <<On a clear moonlit night in 1846, Macedonio Melloni (1798–1854) took a magnificent lens out to the balcony of his apartment in Naples. He had just received the lens, one meter in diameter and the finest he had acquired so far for the Osservatorio Metereologico then under his direction. Melloni expectantly trained the powerfully focused moonlight on his 'thermomultiplier', the most sensitive thermometer yet known to science. To his delight, the thermomultiplier needle swung immediately on receiving the light. Over the ages moonlight had been considered the archetype of 'cold light', famously listed under the heading of 'negative instances of heat' in Francis Bacon's analysis of thermal phenomena designed to illustrate the methods of the new inductive science in the seventeenth century. Marc-Auguste Pictet in the late eighteenth century focused moonbeams into a bright light, but still detected no heat. Now Melloni had finally shown the fallacy of the old opinion. Only moments later, however, Melloni's delight turned into puzzlement as he noticed that the direction of the needle-swing indicated a cooling of the thermometer by the moonlight. That would not do. Melloni considered possible sources of error, made calculations, and cajoled the instruments, repeating the trials until he managed to produce a repeatable detection of a positive heating effect. This was not a frivolous experiment. Melloni was at the height of a productive research career that earned him the epithet of 'the founder of the science' of radiant heat, even 'the Newton of heat'. He made the moonlight experiment with a very specific purpose in mind: Melloni needed moonlight to have heat, in order to uphold his recent conversion to the view that illumination and radiant heat were both effects of one and the same cause. The radiation of heat (unmediated, near instantaneous transfer of heat) had been the subject of active research at least since about 1790, but the nature of radiant heat had still not been elucidated thoroughly. Melloni's importance in the history of science now rests mostly on his contributions toward the identification of radiant heat as long-wavelength light, but curiously he had spent the 1830s piling up experiment after experiment that went against the idea that 'obscure radiant heat' was 'invisible light'. His experimental arguments had convinced many others to turn away from the apparently absurd notion of non-illuminating light.>> end quote a reconstruction of a historical experiment https://youtu.be/iDcy21D6LLc Harry