If the weather is uncomfortably hot on Shabbat, is it permissible to ask a non-Jew, such as a housekeeper, to turn on the air conditioning?
Halacha regards hot weather as a source of "Sa’ar" (discomfort, or distress), as the Pasuk says, "En Nistar Me’hamato" ("no one can hide from its heat" – Tehillim 19:7). One can protect himself from the cold by wearing thick clothing, but there is no escaping the heat. As such, Hacham Ovadia Yosef ruled that asking a non-Jew to activate an air conditioner falls under the category of "Shebut De’shbut Be’makom Sa’ar" (a Rabbinic prohibition within another Rabbinic prohibition in a situation of discomfort). Hacham Ovadia maintained that creating an electrical circuit on Shabbat does not violate a Torah prohibition, and is forbidden only by force of Rabbinic enactment (which was also the view of Rav Shlomo Zalman Auerbach), and asking a gentile to perform an activity forbidden on Shabbat is also forbidden by force of Rabbinic enactment. Hence, asking a gentile to activate electricity would constitute a "Shebut De’shbut," which is permissible in a situation of "Sa’ar." Therefore, as Hacham Ovadia rules in Hazon Ovadia (listen to audio recording for precise citation), it is permissible under hot conditions on Shabbat to ask a gentile to turn on an air conditioner. This is also the ruling of Shemirat Shabbat Ke’hilchatah (13:39). Although Hacham Bension Abba Shaul (Israel, 1923-1998) ruled stringently on this issue, Hacham Ovadia disagreed, and allowed asking a gentile to activate an air conditioner.
Summary: When the weather is uncomfortably hot on Shabbat, one may ask a non-Jew to turn on the air conditioner.