Citing HaRav HID"A and Hakham 'Ovadiah A"H, HaRav Eliyahu Mansour states in his Daily Halacha that:
The Hid"a [...] writes that it is permissible to ask a non-Jew to place a pot of cold liquid on a covered flame on Shabbat [...] because the aforementioned ruling of the Shulhan Aruch is not the only view on the subject. The Rambam [...] was of the opinion that even when it comes to liquids, reheating is distinct from cooking. In his view, once a solid or liquid food has been cooked, it can never be “cooked” again in the Halachic sense, even after it has cooled. Although the Shulhan Aruch does not accept this view, we may nevertheless rely on it to permit asking a gentile, such as a non-Jewish housekeeper, to reheat a pot of hot food, as long as the fire is covered or if the pot is placed on an electric hotplate. Hacham Ovadia Yosef, in several contexts, accepts this ruling of the Hid”a.
If I am not mistaken, the permissibility of reheating a liquid on Shabbat is a question of if "yesh bishul ahhar bishul belahh" (it is possible to recook a liquid after it has already been cooked) and I believe the Halakhic debate on the matter renders the law a Safeq MiDe'Oraita (uncertainty concerning a Biblical law).
I read recently in Yalqut Yosef (Hilkhot Shabbat, Volume 1, though I don't have Siman handy) that asking a Gentile do perform melakhah on Shabbat (e.g. to turn on/off lights) for a Jew's benefit is Rabbinically forbidden. If, for example, it is prohibited to ask a Gentile to turn on/off lights for a Jew's benefit on Shabbat, how is it permissible according to HID"A and Hakham 'Ovadiah to ask a Gentile to perform a melakhah categorized as a Safeq MiDe'Oraita (i.e. reheating food on a hotplate)?