Answer and Explanation:
A cup of tea/coffee transfers heat via conduction, convection and radiation.
Conduction:
Heat transfer from a coffee to the spoon is in direct contact
Inner part of the tea cup against hot liquid will transfer heat to the outer part and saucer.
Convection:
Movement of molecules within the coffee. Hot molecules of the tea at the middle of the drink will be eventually make their way to the outer part of the drink near the tea cup, where they will loose their heat.
Radiation:
Thermal radiation is the loss of heat from a solid object in to atmosphere via the release of electromagnetic radiation. So hot outer edge of the teacup loss the energy to its surroundings via thermal radiation.