Can one move an item that’s plugged into a wall, such as a hot plate that’s on a timer and after it shuts off, can one move it to make room on the counter?
Yes: The fact that the item is plugged in does not make it muktzeh, and it is permitted to move the item provided there are no other reasons for a muktzeh restriction.
Many poskim discuss the status of electrical appliances such as fans, electric blankets, and so on, and the fact that these items are plugged into the wall is not mentioned as a factor in determining their status. See Iggros Moshe (Orach Chaim 5, no. 23), and see Piskei Teshuvos (108:4) who cites different opinions on the matter (some maintain that a fan is a keli she-melachto heiter, and some that it is considered she-melachto issur).
Once off, the hot plate will thus be classified at worse as a keli she-melachto issur, and it will be permitted to move it for need of its place or its use.
For some more references on this issue please see here [Hebrew].