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 \sim 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 \times 10 ^ { 32 } erg s ^ { -1 } and a dissipation time-scale that is only a factor of 3 smaller than the flow crossing time-scale .