a question about the method of heat transfer

(a)
Cold air from the air conditioner will sink as density of cold air is higher than that of warm air, as a result, cold air sinks, warm air rises and flow into the air conditioner installed in the high position near the ceiling and after heat exchange in the air conditioner and becomes cold air, and thus forms a natural circulation of air.
the dominant method of heat transfer : convection

(b)
As metal stool is a better conductor of heat than wood stool, metal stool transfers heat from the body sitting on it more efficiently than wood stool. Typically, the temperature of body is generally higher than the surrounding. Thus when sitting on a metal stool one will lose heat more readily than on a wood stool, as a result colder feeling will resulted.
the dominant method of heat transfer : conduction

(c)
Energy will travel from the sun to earth in forms of radiation (infra-red spectrum). Under the sun. a person will receive radiation more readily, and more energy is absorbed by the body, as a result, the person will feel warmer.
the dominant method of heat transfer : radiation

I hope this can help your understanding. :)

Heat can transfer with or without media.