  We describe a new mechanism that leads to the destabilisation of
non-axisymmetric waves in astrophysical discs with an imposed radial
temperature gradient. This might apply, for example, to the outer parts of
protoplanetary discs. We use linear density wave theory to show that
non-axisymmetric perturbations generally do not conserve their angular momentum
in the presence of a forced temperature gradient. This implies an exchange of
angular momentum between linear perturbations and the background disc. In
particular, when the disturbance is a low-frequency trailing wave and the disc
temperature decreases outwards, this interaction is unstable and leads to the
growth of the wave. We demonstrate this phenomenon through numerical
hydrodynamic simulations of locally isothermal discs in 2D using the FARGO code
and in 3D with the ZEUS-MP and PLUTO codes. We consider radially structured
discs with a self-gravitating region which remains stable in the absence of a
temperature gradient. However, when a temperature gradient is imposed we
observe exponential growth of a one-armed spiral mode (azimuthal wavenumber
$m=1$) with co-rotation radius outside the bulk of the spiral arm, resulting in
a nearly-stationary one-armed spiral pattern. The development of this one-armed
spiral does not require the movement of the central star, as found in previous
studies. Because destabilisation by a forced temperature gradient does not
explicitly require disc self-gravity, we suggest this mechanism may also affect
low-frequency one-armed oscillations in non-self-gravitating discs.
