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Ice-sheet flows can be channelled by perturbations in the basal topography or in the sliding coefficient. These lead to spatial variation in the steady profile, the flux and the dissipative heating. This paper examines the linearized theory of heating variations, showing that the map plane aspect ratio of the basal perturbation has a dominating effect on the qualitative behaviour. For ribbing transverse to the direction of flow, maximum heating occurs over bedrock and sliding viscosity highs. When flow-parallel channelling occurs maximum heating occurs over bedrock lows and sliding viscosity lows. These results are used to examine symmetry-breaking behaviour of numerical thermoviscous ice-sheet models in terms of a dissipation-driven creep instability.