Composite materials have been increasingly used in automotive and aircraft industries, naturally leading to active researches on the materials. Carbon-epoxy composites, one of major composite materials, are investigated to determine their thermal characteristics. Under conditions of thermal fatigues composed of repeated heatings and coolings, variations of elastic constants are studied for the carbon-epoxy composites to reveal the thermal nature of the composites. In general, composite materials are known to have decreasing elastic constants with increasing temperatures. However, in contrary to this commonly observed behavior, the results obtained in this investigation for the elastic constants of the carbon-epoxy composites show unexpected phenomena in that the elastic constants initially increase with increasing temperatures to certain point and decrease later with further increase in temperatures when the carbon-epoxy composites are subjected to thermal fatigues.