  Giant molecular clouds contain supersonic turbulence and magnetohydrodynamic
simulations predict that this turbulence should decay rapidly. Such turbulent
dissipation has the potential to create a warm (T ~100 K) gas component within
a molecular cloud. We present observations of the CO J = 5-4 and 6-5
transitions, taken with the Herschel Space Observatory, towards the Perseus
B1-East 5 region. We combine these new observations with archival measurements
of lower rotational transitions and fit photodissociation region models to the
data. We show that Perseus B1-E5 has an anomalously large CO J = 6-5 integrated
intensity, consistent with a warm gas component existing within the region.
This excess emission is consistent with predictions for shock heating due to
the dissipation of turbulence in low velocity shocks with the shocks having a
volume filling factor of 0.15 per cent. We find that B1-E has a turbulent
energy dissipation rate of 3.5 x 10$^{32}$ erg / s and a dissipation time-scale
that is only a factor of 3 larger than the flow crossing time-scale.
