The question was posed to Hacham Ovadia Yosef as to whether it is permissible to use an electric blanket on Shabbat. Some people use electric blankets either for additional warmth or to help them sleep, and one might have thought that such blankets, which are connected to an electrical source, might be considered Mukseh and thus forbidden to be handled on Shabbat. Additionally, there is the risk that while sleeping one might turn over and pull out the plug or turn off the switch.
Hacham Ovadia, however, in his Yehaveh Da’at (vol. 5, Orah Haim 28), rules that it is entirely permissible to use such a blanket on Shabbat, provided, of course, that it is plugged in and turned on before Shabbat. He writes that such a blanket is not considered Mukseh because its primary function is to serve as an ordinary blanket, which is of course a permissible purpose, and thus it cannot be considered Mukseh. As for the possible claim that the use of an electric blanket disgraces Shabbat, Hacham Ovadia dismisses this argument, noting that an electric blanket differs from electric appliances, because, as mentioned, its primary purpose is to cover a person as he sleeps, and it can be used even without the electric current. And although there is the possibility that one might unwittingly turn the button or pull out the plug as he sleeps, Hacham Ovadia writes that this is considered "Mit’asek" – an act that one has no intention to perform. One is allowed to go to sleep on Shabbat, and if in his sleep he rolls over and turns a switch, he has not done anything wrong.
This is also the ruling of Rabbi Moshe Halevi (Israel, 1961-2001), in his Menuhat Ahaba (listen to audio recording for precise citation), where he notes that it is preferable to place a piece of tape over the button or dial to ensure that one does not accidentally turn it on Shabbat. He also notes that one who is stringent in this regard and does not use an electric blanket "is deserving of blessing" ("Tabo Alav Beracha"), but as for the final Halacha, we follow Hacham Ovadia’s ruling that it is entirely permissible.
Summary: It is permissible to use an electric blanket on Shabbat, provided, of course, that it is plugged in and turned on before Shabbat. One should preferably place some tape over the button or dial to avoid the possibility of unwittingly turning it off on Shabbat.