Final answer:
The necessary conditions for energy transfer by heat to occur through conduction are temperature difference and physical contact.
Step-by-step explanation:
Heat conduction is the transfer of heat between two objects in direct contact with each other. The rate of heat transfer is proportional to the temperature difference and the contact area, and inversely proportional to the distance between the objects. Therefore, the necessary conditions for energy transfer by heat to occur through conduction are temperature difference and physical contact (option a).