  The origin and heating mechanisms of warm (50<T<200 K) molecular gas in
low-mass young stellar objects (YSOs) are strongly debated. Both passive
heating of the inner collapsing envelope by the protostellar luminosity as well
as active heating by shocks and by UV associated with the outflows or accretion
have been proposed. We aim to characterize the warm gas within protosteller
objects, and disentangle contributions from the (inner) envelope, bipolar
outflows and the quiescent cloud. High-J CO maps (12CO J=6--5 and 7--6) of the
immediate surroundings (up to 10,000 AU) of eight low-mass YSOs are obtained
with the CHAMP+ 650/850 GHz array receiver mounted on the APEX telescope. In
addition, isotopologue observations of the 13CO J=6--5 transition and [C I]
3P_2-3P_1 line were taken. Strong quiescent narrow-line 12CO 6--5 and 7--6
emission is seen toward all protostars. In the case of HH~46 and Ced 110 IRS 4,
the on-source emission originates in material heated by UV photons scattered in
the outflow cavity and not just by passive heating in the inner envelope. Warm
quiescent gas is also present along the outflows, heated by UV photons from
shocks. Shock-heated warm gas is only detected for Class 0 flows and the more
massive Class I sources such as HH~46. Outflow temperatures, estimated from the
CO 6--5 and 3--2 line wings, are ~100 K, close to model predictions, with the
exception of the L~1551 IRS 5 and IRAS 12496-7650, for which temperatures <50 K
are found. APEX-CHAMP+ is uniquely suited to directly probe a protostar's
feedback on its accreting envelope gas in terms of heating, photodissociation,
and outflow dispersal by mapping 1'x1' regions in high-J CO and [C I] lines.
