Can heat be considered as a form of potential energy?

When ice melts, its temperature does not rise and hence its kinetic energy remains constant. The amount of energy taken by the ice is used in deriving the molecules of ice apart and it is stored in the form of potential energy. Thus, heat can be said as a form of potential energy.

Heat, the form of potential energy.

Can a room be cooled by leaving the door of an electric refrigerator open in a closed room?

A refrigerator is a heat engine which works in opposite to other heat engines like petrol engine and diesel engine. Thus, a refrigerator extracts heat from the freezing chamber, some work is done on it by electric motor and rejects heat into the surrounding air, thus warming the air. Therefore if the door of a running refrigerator is left open, the room will not be cooled down but instead heated slightly.