No, convection needs an atmosphere to work in, be it gas or liquid, the heatt from the ground we walk on comes from radiant heat that travels through vacuums, you need molecules for convection, in space vacuum theres no molecules to expand and bump into eachother, the warm air only stays warm until it rises and loses the heat within and then falls back to earth due to the weight of the balloon and basket attached, remember the higher you go the colder and less dense it gets, also the heat from within the warth comes up too due to plate techtonics which again works on friction and convection in