We present APEX 218 GHz observations of molecular emission in a complete sample of embedded protostars in the Ophiuchus star-forming region . To study the physical properties of the cores , we calculate H _ { 2 } CO and c - C _ { 3 } H _ { 2 } rotational temperatures , both of which are good tracers of the kinetic temperature of the molecular gas . We find that the H _ { 2 } CO temperatures range between 16 K and 124 K , with the highest H _ { 2 } CO temperatures toward the hot corino source IRAS 16293-2422 ( 69–124 K ) and the sources in the \rho Oph A cloud ( 23–49 K ) located close to the luminous Herbig Be star S 1 , which externally irradiates the \rho Oph A cores . On the other hand , the c - C _ { 3 } H _ { 2 } rotational temperature is consistently low ( 7–17 K ) in all sources . Our results indicate that the c - C _ { 3 } H _ { 2 } emission is primarily tracing more shielded parts of the envelope whereas the H _ { 2 } CO emission ( at the angular scale of the APEX beam ; 3600 au in Ophiuchus ) mainly traces the outer irradiated envelopes , apart from in IRAS 16293-2422 , where the hot corino emission dominates . In some sources , a secondary velocity component is also seen , possibly tracing the molecular outflow .