A reflow soldering apparatus includes a plurality of heating compartments connected in series for heating objects for soldering; transporting means for successively carrying the objects through the compartments; and at least first and second cooling compartments connected subsequent to the heating compartments for cooling the soldered objects. The first cooling compartment subjects the objects to a first, descending temperature gradient, and the second cooling compartment subjects the objects to a second, descending temperature gradient, wherein the second temperature gradient is steeper than the first temperature gradient. The objects are cooled in the first cooling chamber to a temperature below the solidification temperature of the solder.