Hatmana
The third Rabbinic restriction (the first two being Shehiya and Hazara) regarding cooking on Shabbat is called Hatmana, or insulating food. One category of insulation is a material which acts endothermically, that is, the more heat that is supplied to it, the more heat it produces itself. This is known as Davar Hamosif Hevel. The classic example of an endothermic insulating material in the Gemara is olive pits. The Rabbis forbade insulating food with such material, even if it is done before Shabbat, lest one stoke the source from which the insulating material is deriving its heat.
It appears that nowadays, the crockpot would be a modern-day example of an endothermic insulating vessel and according to the ruling of the Rabbis, should be forbidden to use on Shabbat. Indeed, Rabbi Shlomo Zalman Aurerbach, in his last ever responsum, writes that crockpots are forbidden specifically for this reason, and although the top of the crockpot is revealed, nevertheless, the majority of the crockpot is covered.. Nevertheless, Rabbi Ovadia Yosef (Hazon Ovadia, vol. I, pg. 64) rules leniently and gives two reasons. Firstly, he relies on an opinion cited by the Rishonim who say that the restriction on Davar Hamosif Hevel only applies if the food contained within will be eaten at night, not the following day. Furthurmore, one can combine the opinion of the Rama that Hatmana is only applicable when the pot is fully covered by insulating material. However, the crockpot is open on top, only to be covered by the cover of the pot, with no other insulating material.
For those who wish to be more stringent, there are crockpots on the market which have a heating element on the bottom, similar to a heating plate, thus the rest of the crockpot is revealed. Others place empty tin cans under the crockpot in order to elevate the pot, thus causing the crockpot not to be fully covered.
Another category of insulation is known as Matmana Mehamat Davar Aher, which means that the material is being heated by another source, not intrinsically. Although the Shulhan Aruch (258:8) considers this as an insulating agent that is forbidden from Erev Shabbat, nevertheless, the Ramban and other Rishonim write that such insulation is permitted. Indeed, the logstanding Sephardic custom was like the Ramban, and not like the ruling of the Shulchan Aruch. Therefore, the custom in Morocco and many Sephardic lands was to insulate pots of food by wrapping them in blankets. As such, Rabbi Moshe Berdugo (Devar Moshe, 64), Rabbi Ben Zion Abba Shaul (Or LeZion, vol. II, ch. 17,§10 ) Rabbi Ovadia Yosef (Yabia Omer, vol. VI, Orah Haim, § 33) and Rabbi Shalom Messas (Shemesh Umagen, vol. III, § 50) all write that one is permitted to wrap up pots in blankets and the like to insulate the food contained within.
Summary: There is a Halachic basis to permit using crockpots on Shabbat. One may wrap pots of food to keep them insulated over Shabbat.