  We study the properties of bright and vortex solitons in thermal media with
nonuniform thermal conductivity and homogeneous refractive index, whereby the
local modulation of the thermal conductivity strongly affects the entire
refractive index distribution. While regions where the thermal conductivity is
increased effectively expel light, self-trapping may occur in the regions with
reduced thermal conductivity, even if such regions are located close to the
material boundary. As a result, strongly asymmetric self-trapped beams may form
inside a ring with reduced thermal conductivity and perform persistent rotary
motion. Also, such rings are shown to support stable vortex solitons, which may
feature strongly non-canonical shapes.
