doorway fan
A doorway fan is a small electric fan, mounted in the upper corner of a doorway, that moves air from one room to another and thereby helps equalize temperatures in both rooms; typically the motor in the fan is reversible. One of the problems with a solid-fuel fireplace or stove is that although it may heat the room it is in very well, it may leave other rooms cold. Doorway fans are a convenient way of getting around this problem by circulating warm air to other parts of the house. They are cheap to run and can pay for their purchase cost within a single heating system.
Disadvantages of doorway fans is that they do slightly obstruct, and may detract from the appearance of, a doorway. The amount of noise they make varies from one model to another.