We construct the gravitational dual of a one-parameter class of states of strongly coupled $SU(N)$ $N=4$ SYM at infinite $N$ and asymptotic temperature $T\infty$, on a fixed Schwarzschild black hole background with temperature $T\mathrm{BH}$. The resulting bulk geometry is of the flowing type and allow us to measure Hawking radiation at strong coupling. The outgoing Hawking flux is a function of the dimensionless ratio $\tau \equiv T\infty /T\mathrm{BH}$ and appears to be non-monotonic in $\tau$. At present, we have no field theory understanding for this behaviour.