We have developed a thermal insulation based on bi-component fibers that adapts to its thermal environment, providing greater insulation at low temperatures than at warmer temperatures. The analysis of bi-metallic strips done by Timoshenko [1] for strips of rectangular cross-section concluded that “…curvature is proportional to the difference in elongation of the two metals and inversely proportional to the thickness of the strip.” We have extended Timoshenko’s formulation and applied it to bi-component fibers of circular and triangular cross-sections. In each case, the curvature resulting from the balance of the axial forces and bending moments has been brought into a standard form inversely proportional to (A+Bn+C/n) where n is the ratio of the moduli and A, B, and C are functions of the geometry of the two components. An important consequence of this result is that for any “n” there is a maximum curvature where (A+Bn+C/n) is a minimum. We have used the process of melt-spinning to produce fibers with circular and triangular cross-sections, varying the proportion of the two components. The polymers used have widely different coefficients of thermal expansion. These fibers spontaneously form mats at room temperatures. The experimentally measured thickness changes are in good agreement with the analytical results for fiber bending. The most effective samples to date change thickness by more than 1.5% per degree C (30% over a temperature range from approximately 20°C to 0°C).