Experiments on a superconducting single-electron transistor are reported. A new structure in the current-voltage characteristics at subgap voltages was observed when temperature was not too low as compared to the superconducting transition temperature Tc of the sample. The strength of the anomalies increases exponentially with temperature. The dominating features arise from matching of singularities in the density of states on two sides of a tunnel junction, and from the Josephson-quasiparticle cycle. Thermal excitations are essential for the former process, and they also make the latter process possible at low voltages.