If you burn your hand grabbing a hot cup of coffee, what type of thermal energy transfer has taken place?

Conduction Mode of Heat Transfer

Explanation:

When transfer of heat requires medium to transmit heat from one end to other end then this may be due to (i) Conduction or (ii) Convection

While it do not require any medium to transmit heat in Radiation mode of heat transfer.

So here in the given example we are holding a cup of tea so here thermal energy is transferred by the medium of cup from Tea to our hand.

When medium particles move from one position to other position along with thermal energy then this is known as convection mode of heat transfer while in conduction mode of heat transfer we know that medium particles remains at their own position and heat is transferred from one point to other.

So here in this example the heat is transferred through the medium of cup which and the molecules of cup do not move. So here energy transfer is by CONDUCTION mode of heat transfer