Final answer:
The angle at which a temperature contour intersects an insulated boundary in a homogeneous material should be perpendicular to the boundary.
Step-by-step explanation:
The angle at which a temperature contour in a homogeneous material intersects an insulated boundary should always be perpendicular to the boundary. This is because the heat transfer in a material occurs through conduction, and perpendicular direction of the contour allows for the most efficient heat transfer.
The rate of heat transfer by conduction is directly proportional to the temperature difference, surface area, and substance's conductivity. It is inversely proportional to the thickness of the material.