To improve the fuel efficiency of automobile engines and reduce pollution owing to automobile exhaust, this study discusses a fixed-curvature spiral-coil heat exchanger that recovers exhaust heat. Herein, the heat transfer performance of the spiral coil is studied via experimental testing and numerical simulation. In this study, a new type of variable-curvature spiral coil is designed to improve the efficiency of the heat exchanger. The effect of different conical angles on the resistance and heat transfer performance of the spiral coil within a range of Reynolds numbers of 4000–14,000 was analyzed. The heat exchange efficiency is a combination of the convective heat transfer and the overall heat recovery. The results of this study indicate that for a spiral-coil tube of length L, increasing the cone angle improves the convective heat transfer outside the tube. However, as the flow resistance increases, the exhaust heat recovery of a variable-curvature spiral-coil heat exchanger (VSE) is up to 18.8% higher than that of a constant curvature spiral-coil heat exchanger. The combined performance of VSE is excellent when the cone angle is 15 deg.