Three-dimensional physical and mathematic models are established for the internal heat transfer in a defective furnace. The temperature distribution and infrared characteristics of the surface when the defect in a furnace is detected in different positions are studied. The analysis result shows that the firebricks play a major role in the thermal insulation of the furnace. When the firebricks break down, the temperature of the outer surface of the furnace is abnormal. In the position of the defect, the difference between the maximum temperature and the normal operation temperature increases exponentially with the defect depth.