Model calculations of the electrodynamic properties of superconducting composites are usually carried out assuming that the material constants, such as critical current density and resistivity, are uniform over the cross-section of the composite, or at least rotationally symmetric. Also, the applied field is usually considered to be uniform over a distance compared to the composite diameter. In this paper the possibility will be discussed that non-uniformity in field and material properties may cause significant non-uniformity in heat production so to disturb the local temperature pattern and form sources of instabilities and quenches. The influence of the cooling conditions on the transport current-carrying capacity in the a.c. regime is also discussed
