Temperature-dependent current-voltage measurements are used to determine the dominant recombination mechanism in thin-film heterojunction solar cells based on Cu(In,Ga)(S,Se)2 absorbers with chemical bath deposited ZnS buffer layer. The measurements are carried out in the dark and under illumination in the temperature range 200-320 K. The activation energy of the recombination under illumination follows the absorber band gap energy Eg=1.07eV of bulk Cu(In,Ga)(S,Se)2. The thermal dependence of the diode ideality factor is described by classical Shockley-Read-Hall (SRH) recombination via an exponential distribution of trap states in the bulk of the absorber. In the dark, the current flow is dominated by tunnelling enhanced bulk recombination with a tunnelling energy E00=18meV. Two activation energies higher than Eg, namely 1.21 and 1.40eV, have been found. These results may be explained by dominant recombination in a region close to the surface of the Cu(In,Ga)(S,Se)2 absorber with an enlarged band gap. Thus, the electronic loss in the ZnO/Zn(S,OH)/Cu(In,Ga)(S,Se)2 solar cell takes place mainly in the absorber and is determined by tunnelling enhanced bulk recombination with a tunnelling energy E00 influenced by illumination.