i am still unclear as to what your inquiry about the solar constant is about. but here is evidence which shows that past trends indicate that we should now be heading into an ICE age, not a warming period. thus we may conclude that the current warming period is not due to a natural cycle of a little ice age or any other kind of ice age.


http://www.aip.org/history/climate/cycles.htm


Since the Milankovitch cycles could be computed directly from celestial mechanics, one could project them forward in time, as Emiliani had done in 1966. In 1972, presenting more Caribbean cores, he again advised that "the present episode of amiable climate is coming to an end." Thus "we may soon be confronted with... a runaway glaciation." However, he added, greenhouse effect warming caused by human emissions might overwhelm the orbital shifts, so we might instead face "a runaway deglaciation."(25)
Some other scientists agreed that the current interglacial warm period had peaked 6,000 or so years ago, and should be approaching its natural end. A prominent example was Kukla, continuing his study of loess layers in Czechoslovakia. He could now date the layers thanks to a new technique provided by other scientists. Geological and oceanographic studies had shown that over the course of millions of years, now and then the Earth's entire magnetic field flipped: the North magnetic pole became the South magnetic pole and vice-versa. These reverses were recorded where layers of sediment or volcanic lava had entombed the direction of the magnetic field at the time. Geologists had worked out a chronology in lava flows, dated by the faint radioactivity of an isotope of potassium that decayed very slowly.(26) If even one magnetic-field reversal could be identified in any set of layers, it pinned down the timing of the entire sequence. When the loess layers were dated in this fashion, Milankovitch cycles turned up. Extrapolating the cycles into the future, Kukla thought the next shift to an ice age "is due very soon."(Link from below)(27)

Celcius, I think you are mistaken.