Jewish law forbids cooking of *any* kind on shabbos, be it on an open fire,
an oven, a radiator, the sun... Cholent is not cooked on Shabbos; rather it
must be sufficiently cooked before Shabbos. The actual measure is one third
fully cooked to qualify as being sufficient. This measure is known in the
Talmud as Ma'achal Ben Drosi (food of Ben-Drosi), who was a thief, always on
the run. He only had time to cook his food to the level of one-third. As
anyone will tell you, however, the cholent does improve as it is left on the
heat-source over shabbos. This does not constitute cooking, as "ein bishul
achar bishul" (lit. no cooking after cooking - once the food is cooked, it
will not be cooked any more).
By the way, regarding your comparison between Solar heat and heat from a
stove, here in Israel most orthodox rabbis have forbidden the use of water
from solar heaters, the most popular way of using the heat from the sun.
with Torah blessings,