The efficiency of electron cooling can be improved by adiabatically expanding the electron beam in a decreasing magnetic field, thereby lowering the transverse electron temperature. An electron beam expanded by a factor of 10 has been implemented at the CRYRING electron cooler, decreasing the transverse electron temperature from 100 to 10 meV. This has resulted in an increased drag force between ions and electrons and in large reductions of cooling times. Also, the energy resolution in electron-ion recombination experiments at low relative energy has increased by a factor of 10.