The apparatus is arranged to supply a flow of substantially pure oxygen to a person, and comprises a source of substantially pure oxygen gas, means for release of the substantially pure oxygen gas from the source into an ambient atmosphere; and means for cooling the substantially pure oxygen gas released from the source to a temperature below that of the ambient atmosphere. The substantially pure oxygen gas when cooled by the cooling means can be allowed to sink under ambient pressure by convection into a zone including the ambient atmosphere, the zone being beneath, and in convective communication with, the cooled substantially pure oxygen gas, whereby the cooled and sunken substantially pure oxygen gas can come into contact with the skin of a person in that zone. At least one parameter (such as temperature, oxygen concentration, sound or vibration) is monitored in the zone and operation of the release means is only permitted when the parameter is in a predetermined range.