  The solar wind undergoes significant heating as it propagates away from the
Sun; the exact mechanisms responsible for this heating are not yet fully
understood. We present for the first time a statistical test for one of the
proposed mechanisms, stochastic ion heating. We use the amplitude of magnetic
field fluctuations near the proton gyroscale as a proxy for the ratio of
gyroscale velocity fluctuations to perpendicular (with respect to the magnetic
field) proton thermal speed, defined as $\epsilon_p$. Enhanced proton
temperatures are observed when $\epsilon_p$ is larger than a critical value
($\sim 0.019 - 0.025$). This enhancement strongly depends on the proton plasma
beta ($\beta_{||p}$); when $\beta_{||p} \ll 1$ only the perpendicular proton
temperature $T_{\perp}$ increases, while for $\beta_{||p} \sim 1$ increased
parallel and perpendicular proton temperatures are both observed. For
$\epsilon_p$ smaller than the critical value and $\beta_{||p} \ll 1$ no
enhancement of $T_p$ is observed while for $\beta_{||p} \sim 1$ minor increases
in $T_{\parallel}$ are measured. The observed change of proton temperatures
across a critical threshold for velocity fluctuations is in agreement with the
stochastic ion heating model of Chandran et al. (2010). We find that
$\epsilon_p > \epsilon_{\rm crit}$ in 76\% of the studied periods implying that
stochastic heating may operate most of the time in the solar wind at 1 AU.
