The suppression of (neoclassical) tearing modes is of great importance for the success of future fusion reactors like ITER. Electron cyclotron waves can suppress islands, both by driving noninductive current in the island region and by heating the island, causing a perturbation to the Ohmic plasma current. This Letter reports on experiments on the TEXTOR tokamak, investigating the effect of heating, which is usually neglected. The unique set of tools available on TEXTOR, notably the dynamic ergodic divertor to create islands with a fully known driving term, and the electron cyclotron emission imaging diagnostic to provide detailed 2D electron temperature information, enables a detailed study of the suppression process and a comparison with theory.