The above methods of forming a fog all require cooling the air. FOG - formed by mixing two unsaturated air masses. Moist air coming out of your mouth is an example of mixing fog. Contrails are another example. Saturation vapor pressure depends on the temperature - the higher the temperature the higher the saturation vapor pressure.
Warm rain falling into a cool air mass near the surface can form a fog.
An example of such a fog is the type that forms in the vicinity of warm fronts. The colder air directly above the water is heated from below and rises forming what appears to be steam. Observed over unfrozen lakes in autumn or winter. Steam fog also forms above a wet surface on a sunny day - over a road after a summer rain shower. The air near the ground warms lowering the relative humidity.