It is important to understand the concepts of heat transfer in order to explain why a wooden spoon dipped in an ice cream cup does not become cold. Heat transfer can occur through three main mechanisms: conduction, convection, and radiation. Let's discuss each of these mechanisms in detail and explain why they do not apply in this scenario.

1. Conduction:
Conduction is the transfer of heat through direct contact between two objects, where heat flows from a hotter object to a colder one. In this case, the wooden spoon would need to be in direct contact with the ice cream cup for conduction to occur. However, wood is a poor conductor of heat compared to other materials like metal or glass. The low thermal conductivity of wood means that it does not easily transfer heat from the ice cream to itself, and therefore, the spoon does not become cold through conduction.

2. Convection:
Convection is the transfer of heat through the movement of a fluid. It requires the presence of a fluid medium, such as air or liquid, to carry heat from one place to another. Since the ice cream cup does not contain any fluid that can circulate and carry heat, convection does not play a role in cooling the wooden spoon.

3. Radiation:
Radiation is the transfer of heat through electromagnetic waves. All objects emit and absorb radiation to some extent, depending on their temperature. However, radiation requires a temperature difference between two objects for heat transfer to occur. In this case, both the wooden spoon and the ice cream cup are at room temperature, so there is no significant temperature difference to drive radiation heat transfer.

Considering all these factors, the correct answer is option 'D' - the wooden spoon does not become cold when dipped in an ice cream cup. The wooden spoon's temperature remains relatively unchanged because wood is a poor conductor of heat, there is no fluid medium for convection, and there is no significant temperature difference for radiation to occur.