  We investigate a dynamical system consisting of $N$ particles moving on a
$d$-dimensional torus under the action of an electric field $E$ with a Gaussian
thermostat to keep the total energy constant. The particles are also subject to
stochastic collisions which randomize direction but do not change the speed. We
prove that in the van Hove scaling limit, $E\to 0$ and $t\to t/E^2$, the
trajectory of the speeds $v_i$ is described by a stochastic differential
equation corresponding to diffusion on a constant energy sphere. This verifies
previously conjectured behavior. Our results are based on splitting the
system's evolution into a "slow" process and an independent "noise". We show
that the noise, suitably rescaled, converges a Brownian motion, enhanced in the
sense of rough paths. Then we employ the It\^o-Lyons continuity theorem to
identify the limit of the slow process.
