In this example, the bottle, made of plastic, has solid matter that allows for conduction of heat. What happens if in between the juice and the ice water there are no molecules? (Hint, think Yeti)

Conduction of heat would not happen.

Explanation:

Heat transfer by conduction only happens by direct contact of the molecules or atoms of a substance: in a solid, particles cannot travel but only vibrate; the heat conduction happens because the vibration of a particle causes adjacent particles to vibrate.

Also, in that system heat transfer by convection would not happen, since convection requires that the particles travel to transfer the heat.

Only heat transfer by radiation can happen when there are no particles, since infrared radiation travels through the empty space.