To improve the fuel efficiency in automobile engines and reduce automobile exhaust pollution, 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 tests and numerical simulation. 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 (4000–14000) was analyzed. The heat-exchange efficiency is a combination of the convective heat transfer and the overall heat recovery. Results 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°.