Rapidly rotating neutron stars in low-mass X-ray binaries may be an interesting source of gravitational waves (GWs). In particular, several modes of stellar oscillation may be driven unstable by GW emission, and this can lead to a detectable signal. Here we illustrate how current X-ray and ultraviolet observations can constrain the physics of the r-mode instability. We show that the core temperatures inferred from the data would place many systems well inside the unstable region predicted by standard physical models. However, this is at odds with theoretical expectations. We discuss different mechanisms that could be at work in the stellar interior, and we show how they can modify the instability window and make it consistent with the inferred temperatures.