  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.
